Engineering Graphics MCQ’S Unit-1

PLANE CURVES AND FREE HAND SKETCHING

CONSTRUCTION OF PARALLEL & PERPENDICULAR LINES

1.Given are the steps to draw a perpendicular
to a line at a point within the line when the
point is near the Centre of a line.
Arrange the steps. Let AB be the line and P
be the point in it
i. P as Centre, take convenient radius R1 and
draw arcs on the two sides of P on the line at
C, D.
ii. Join E and P
iii. The line EP is perpendicular to AB
iv. Then from C, D as Centre, take R2 radius
(greater than R1), draw arcs which cut at E.
a) i, iv, ii, iii
b) iii, ii, iv, i
c) iv, iii, i, ii
d) ii, i, iv, iii
Answer: a

Explanation: Here uses the concept of a locus. Every 2 points have a particular line
that is every point on line is equidistant from
both the points. The above procedure shows
how the line is build up using arcs of the
similar radius.

2.Given are the steps to draw a perpendicular
to a line at a point within the line when the
point is near an end of the line.
Arrange the steps. Let AB be the line and P
be the point in it.
i. Join the D and P.
ii. With any point O draw an arc (more than a
semicircle) with a radius of OP, cuts AB at C.
iii. Join the C and O and extend till it cuts the
large arc at D.
iv. DP gives the perpendicular to AB.
a) i, iv, ii, iii
b) iii, ii, iv, i
c) iv, iii, i, ii
d) ii, iii, i, iv
Answer: d
Explanation: There exists a common
procedure for obtaining perpendiculars for
lines. But changes are due changes in
conditions whether the point lies on the line,
off the line, near the centre or near the ends
etc.
3.Given are the steps to draw a perpendicular
to a line at a point within the line when the
point is near the centre of line.
Arrange the steps. Let AB be the line and P
be the point in it
i. Join F and P which is perpendicular to AB.
ii. Now C as centre take the same radius and
cut the arc at D and again D as centre with
same radius cut the arc further at E.
iii. With centre as P take any radius and draw
an arc (more than a semicircle) cuts AB at C.
iv. Now D, E as centre take radius (more than
half of DE) draw arcs which cut at F.
a) i, iv, ii, iii
b) iii, ii, iv, i
c) iv, iii, i, ii
d) ii, i, iv, iii

Answer: b
Explanation: Generally in drawing
perpendiculars to lines involves in drawing a
line which gives equidistance from either side
of the line to the base, which is called the
locus of points. But here since the point P is
nearer to end, there exists some peculiar steps
in drawing arcs.

4.Given are the steps to draw a perpendicular
to a line from a point outside the line, when
the point is near the centre of line.
Arrange the steps. Let AB be the line and P
be the point outside the line
i. The line EP is perpendicular to AB
ii. From P take convenient radius and draw
arcs which cut AB at two places, say C, D.
iii. Join E and P.
iv. Now from centers C, D draw arc with
radius (more than half of CD), which cut each
other at E.
a) i, iv, ii, iii
b) iii, ii, iv, i
c) iv, iii, i, ii
d) ii, iv, iii, i
Answer: d
Explanation: At first two points are taken
from the line to which perpendicular is to
draw with respect to P. Then from two points
equidistant arcs are drawn to meet at some
point which is always on the perpendicular.
So by joining that point and P gives
perpendicular.

5.Given are the steps to draw a perpendicular
to a line from a point outside the line, when
the point is near an end of the line.
Arrange the steps. Let AB be the line and P
be the point outside the line
i. The line ED is perpendicular to AB
ii. Now take C as centre and CP as radius cut
the previous arc at two points say D, E.
iii. Join E and D.
iv. Take A as center and radius AP draw an
arc (semicircle), which cuts AB or extended
AB at C.
a) i, iv, ii, iii
b) iii, ii, iv, i
c) iv, ii, i, iii
d) ii, iv, iii, i
Answer: c
Explanation: The steps here show how to
draw a perpendicular to a line from a point
when the point is nearer to end of line. Easily
by drawing arcs which are equidistance from
either sides of line and coinciding with point
P perpendicular has drawn.
6.Given are the steps to draw a perpendicular
to a line from a point outside the line, when
the point is nearer the centre of line.
Arrange the steps. Let AB be the line and P
be the point outside the line
i. Take P as centre and take some convenient
radius draw arcs which cut AB at C, D.
ii. Join E, F and extend it, which is
perpendicular to AB.
iii. From C, D with radius R1 (more than half
of CD), draw arcs which cut each other at E.
iv. Again from C, D with radius R2 (more
than R1), draw arcs which cut each other at F.
a) i, iii, iv, ii
b) iii, ii, iv, i
c) iv, iii, i, ii
d) ii, iv, iii, i
Answer: a
Explanation: For every two points there
exists a line which has points from which
both the points are equidistant otherwise
called perpendicular to line joining the two
points. Here at 1st step, we created two on the
line we needed perpendicular, then with equal
arcs from either sides we created the
perpendicular.

7.Given are the steps to draw a parallel line
to given line AB at given point P.
Arrange the steps.
i. Take P as centre draw a semicircle which
cuts AB at C with convenient radius.
ii. From C with radius of PD draw an arc with
cuts the semicircle at E.
iii. Join E and P which gives parallel line to AB. iv. From C with same radius cut the AB at D.

a) i, iv, ii, iii
b) iii, ii, iv, i
c) iv, iii, i, ii
d) ii, iv, iii, i
Answer: a
Explanation: There exists some typical steps
in obtaining parallel lines for required lines at
given points which involves drawing of arcs,
necessarily, here to form a parallelogram
since the opposite sides in parallelogram are
parallel.

8.Given are the steps to draw a parallel line
to given line AB at a distance R.
Arrange the steps.
i. EF is the required parallel line.
ii. From C, D with radius R, draw arcs on the
same side of AB.
iii. Take two points say C, D on AB as far as
possible.
iv. Draw a line EF which touches both the arc
(tangents) at E, F.
a) i, iv, ii, iii
b) iii, ii, iv, i
c) iv, iii, i, ii
d) ii, iv, iii, i
Answer: b
Explanation: Since there is no reference
point P to draw parallel line, but given the
distance, we can just take arcs with distance
given from the base line and draw tangent
which touches both arcs.
9.Perpendiculars can’t be drawn using
a) T- Square
b) Set-squares
c) Pro- circle
d) Protractor
Answer: c
Explanation: T-square is meant for drawing a straight line and also perpendiculars. And also using set-squares we can draw perpendiculars. Protractor is used to measure angles and also we can use to draw perpendiculars. But pro-circle consists of circles of different diameters.

10.The length through perpendicular gives
the shortest length from a point to the line.
a) True
b) False
Answer: a
Explanation: The statement given here is
right. If we need the shortest distance from a
point to the line, then drawing perpendicular
along the point to a line is the best method.
Since the perpendicular is the line which has
points equidistant from points either side of
given line.

DRAWING REGULAR POLYGONS & SIMPLE CURVES

1.A Ogee curve is a
a) semi ellipse
b) continuous double curve with convex and
concave
c) freehand curve which connects two parallel
lines
d) semi hyperbola
Answer: b
Explanation: An ogee curve or a reverse
curve is a combination of two same curves in
which the second curve has a reverse shape to
that of the first curve. Any curve or line or
mould consists of a continuous double curve
with the upper part convex and lower part
concave, like ‘’S’’.

2.Given are the steps to construct an
equilateral triangle, when the length of side is
given. Using, T-square, set-squares only.
Arrange the steps.
i. The both 2 lines meet at C. ABC is required
triangle
ii. With a T-square, draw a line AB with
given length

iii. With 30o-60o set-squares, draw a line
making 60o with AB at A
iv. With 30o-60o set-squares, draw a line
making 60o with AB at B
a) i, iv, ii, iii
b) iii, ii, iv, i
c) iv, iii, i, ii
d) ii, iii, iv, i
Answer: d
Explanation: Here gives the simple
procedure since T-square and 30o
-60o setsquares. And also required triangle is
equilateral triangle. The interior angles are
60°, 60°, 60° (180° /3 = 60°). Set- squares are
used for purpose of 60°.

3.Given are the steps to construct an
equilateral triangle, with help of a compass,
when the length of a side is given. Arrange
the steps.
i. Draw a line AB with given length
ii. Draw lines joining C with A and B
iii. ABC is required equilateral triangle
iv. With centers A and B and radius equal to
AB, draw arcs cutting each other at C
a) i, iv, ii, iii
b) iii, ii, iv, i
c) iv, iii, i, ii
d) ii, iii, iv, i
Answer: a
Explanation: Here gives the simple
procedure to construct an equilateral triangle.
Since we used compass we can construct any
type of triangle but with set-squares it is not
possible to construct any type of triangles
such as isosceles, scalene etc.
4.Given are the steps to construct an
equilateral triangle when the altitude of a
triangle is given. Using, T-square, set-squares
only. Arrange the steps.
i. Join R, Q; T, Q. Q, R, T is the required
triangle
ii. With a T-square, draw a line AB of any
length
iii. From a point P on AB draw a
perpendicular PQ of given altitude length
iv. With 30o-60o set-squares, draw a line
making 30o with PQ at Q on both sides
cutting at R, T
a) i, iv, ii, iii
b) iii, ii, iv, i
c) iv, iii, i, ii
d) ii, iii, iv, i
Answer: d
Explanation: Here gives the simple
procedure since T-square and 30°-60°setsquares. The interior angles are 60°, 60°, 60°
(180° /3 = 60°). Altitude divides the sides of equilateral triangle equally. Set- squares are
used for purpose of 30°.
5.Given are the steps to construct an
equilateral triangle, with help of a compass,
when the length of altitude is given. Arrange
the steps.
i. Draw a line AB of any length. At any point
P on AB, draw a perpendicular PQ equal to
altitude length given
ii. Draw bisectors of CE and CF to intersect
AB at R and T respectively.QRT is required
triangle
iii. With center Q and any radius, draw an arc
intersecting PQ at C
iv. With center C and the same radius, draw
arcs cutting the 1st arc at E and F
a) i, iii, iv, ii
b) iii, ii, iv, i
c) iv, iii, i, ii
d) ii, iii, iv, i
Answer: a
Explanation: This is the particular procedure
used for only constructing an equilateral
triangle using arcs when altitude is given
since we used similar radius arcs to get 30o
on both sides of a line. Here we also bisected
arc using the same procedure from bisecting
lines.

6.How many pairs of parallel lines are there
in regular Hexagon?
a) 2
b) 3
c) 6
d) 1
Answer: b
Explanation: Hexagon is a closed figure
which has six sides, six corners. Given is
regular hexagon which means it has equal
interior angles and equal side lengths. So,
there will be 3 pair of parallel lines in a
regular hexagon.
7.Given are the steps to construct a square when the length of a side is given. Using, T square, set-squares only. Arrange the steps.
i. Repeat the previous step and join A, B, C
and D to form a square
ii. With a T-square, draw a line AB with
given length.
iii. At A and B, draw verticals AE and BF
iv. With 45o set-squares, draw a line making
45o with AB at A cuts BF at C
a) i, iv, ii, iii
b) iii, ii, iv, i
c) iv, iii, i, ii
d) ii, iii, iv, i
Answer: d
Explanation: Square is closed figure with
equal sides and equal interior angles which is
90°. In the above steps, it is given the
procedure to draw a square using set-squares.
45° set-square is used since 90/2 = 45.
8.How many pairs of parallel lines are there
in a regular pentagon?
a) 0
b) 1
c) 2
d) 5
Answer: a
Explanation: Pentagon is a closed figure
which has five sides, five corners. Given is
regular pentagon which means it has equal
interior angles and equal side lengths. Since
five is odd number so, there exists angles 36°,
72°, 108°, 144°, 180° with sides to
horizontal.
9.Given are the steps to construct a square
using a compass when the length of the side
is given. Arrange the steps.
i. Join A, B, C and D to form a square
ii. At A with radius AB draw an arc, cut the
AE at D
iii. Draw a line AB with given length. At A
draw a perpendicular AE to AB using arcs
iv. With centers B and D and the same radius,
draw arcs intersecting at C
a) i, iv, ii, iii
b) iii, ii, iv, i
c) iv, iii, i, ii
d) ii, iii, iv, i
Answer: b
Explanation: Here we just used simple
techniques like drawing perpendiculars using
arcs and then used the compass to locate the
fourth point. Using the compass it is easier to
draw different types of closed figures than
using set-squares.

10.Given are the steps to construct regular
polygon of any number of sides. Arrange the
steps.
i. Draw the perpendicular bisector of AB to
cut the line AP in 4 and the arc AP in 6
ii. The midpoint of 4 and 6 gives 5 and
extension of that line along the equidistant
points 7, 8, etc gives the centers for different
polygons with that number of sides and the
radius is AN (N is from 4, 5, 6, 7, so on to N)
iii. Join A and P. With center B and radius
AB, draw the quadrant AP
iv. Draw a line AB of given length. At B,
draw a line BP perpendicular and equal to AB
a) i, iv, ii, iii
b) iii, ii, iv, i

c) iv, iii, i, ii
d) ii, iii, iv, i
Answer: c
Explanation: Given here is the method for
drawing regular polygons of a different
number of sides of any length. This includes
finding a line where all the centers for regular
polygons lies and then with radius taking any
end of 1st drawn line to center and then
completing circle at last, cutting the circle
with the same length of initial line. Thus we
acquire polygons.

DRAWING TANGENTS AND NORMALS FOR DIFFERENT CONDITIONS OF CIRCLE

1.Given are the steps to draw a tangent to
any given circle at any point P on it. Arrange
the steps.
i. Draw the given circle with center O and
mark the point P anywhere on the circle.
ii. With centers O and Q draw arcs with equal
radius to cut each other at R.
iii. Join R and P which is the required
tangent.
iv. Draw a line joining O and P. Extend the
line to Q such that OP = PQ.
a) i, iv, ii, iii
b) iv, i, iii, ii
c) iii, i, iv, ii
d) ii, iv, i, iii
Answer: a
Explanation: Tangent is a line which touches
a curve at only one point. Every tangent is
perpendicular to its normal. Here we first
found the normal which passes through center
and point. Then drawing a perpendicular to it
gives the tangent.
2.Given are the steps to draw a tangent to
given circle from any point outside the circle.
Arrange the steps.
i. With OP as diameter, draw arcs on circle at
R and R1.
ii. Draw the given circle with center O.
iii. Join P and R which is one tangent and
PR1 is another tangent.
iv. Mark the point P outside the circle.
a) ii, iv, iii, i
b) iv, i, iii, ii
c) iii, i, iv, ii
d) ii, iv, i, iii
Answer: d
Explanation: Usually when a point is outside
the circle there exists two tangents. For which
we first join the center with point P and then
taking distance from center to P as diameter
circle is drawn from the midpoint of center
and P to cut circle at two points where
tangents touch the circle.
3.Given are the steps to draw a tangent to
given arc even if center is unknown and the
point P lies on it. Arrange the steps. Let AB
be the arc.
i. Draw EF, the bisector of the arc CD. It will
pass through P.
ii. RS is the required tangent.
iii. With P as center and any radius draw arcs
cutting arc AB at C and D.
iv. Draw a perpendicular RS to EF through P.
a) ii, iv, iii, i
b) iv, i, iii, ii
c) iii, i, iv, ii
d) ii, iv, i, iii
Answer: c
Explanation: Even if the center of the arc is
unknown, just by taking any some part of arc
and bisecting that with a line at required point
p gives us normal to tangent at P. So then
from normal drawing perpendicular gives our
required tangent.
4.Given are the steps to draw a tangent to
given circle and parallel to given line.
Arrange the steps.
i. Draw a perpendicular to given line and
extend to cut the circle at two points P and Q

ii. At P or Q draw perpendicular to normal
then we get the tangents.
iii. PQ is the normal for required tangent.
iv. Draw a circle with center O and line AB as
required.
a) ii, iv, iii, i
b) iv, i, iii, ii
c) iii, i, iv, ii
d) ii, iv, i, iii
Answer: b
Explanation: Normal of curve will be
perpendicular to every parallel tangent at that
point. We just drawn the longest chord
(diameter) and then perpendicular it gives the
required tangents. Since circle is closed figure
there exist two tangents parallel to each other.

5.How many external tangents are there for
two circles?
a) 1
b) 2
c) 3
d) 4
Answer: b
Explanation: External tangents are those
which touch both the circles but they will not
intersect in between the circles. The tangents
touch at outmost points of circles that are
ends of diameter if the circles have the same
diameter.
6.How many internal tangents are there for
two circles?
a) 4
b) 3
c) 2
d) 1
Answer: c
Explanation: Internal tangents are those
which touch both the circle and also intersect
each other on the line joining the centers of
circles. And the internal tangents intersect
each other at midpoint of line joining the
center of circles only if circles have the same
diameter.

7.For any point on any curve there exist two
normals.
a) True
b) False
Answer: b
Explanation: Here we take point on the
curve. There exist multiple tangents for some
curve which are continuous, trigonometric
curves, hyperbola etc. But for curves like
circles, parabola, ellipse, cycloid etc. have
only one tangent and normal.
8.Arrange the steps. These give procedure to
draw internal tangent to two given circles of
equal radii.
i. Draw a line AB which is the required
tangent.
ii. Draw the given circles with centers O and
P.
iii. With center R and radius RA, draw an arc
to intersect the other circle on the other circle
on the other side of OP at B.
iv. Bisect OP in R. Draw a semi circle with
OR as diameter to cut the circle at A.
a) ii, iv, iii, i
b) iv, i, iii, ii
c) iii, i, iv, ii
d) ii, iv, i, iii
Answer: a
Explanation: Since the circles have same
radius. The only two internal tangents will
intersect at midpoint of line joining the
centers. So we first found the center and then
point of intersection of tangent and circle then
from that point to next point it is drawn a arc
midpoint as center and join the points gave us
tangent.

9.There are 2 circles say A, B. A has 20 units
radius and B has 10 units radius and distance
from centers of A and B is 40 units. Where
will be the intersection point of external
tangents?
a) to the left of two circles
b) to the right of the two circles
c) middle of the two circles
d) they intersect at midpoint of line joining
the centers
Answer: b
Explanation: A has 20 units radius and B has
10 units radius. So, the tangents go along the
circles and meet at after the second circle that
is B that is the right side of both circles. And
we asked for external tangents so they meet
away from the circles but not in between
them.

10.10.There are 2 circles say A, B. A is smaller
than B and they are not intersecting at any
point. Where will be the intersection point of
internal tangents for these circles?
a) to the left of two circles
b) to the right of the two circles
c) middle of the two circles
d) they intersect at midpoint of line joining
the centers
Answer: b
Explanation: A is smaller than B so the
intersection point of internal tangents will not
be on the midpoint of the line joining the
centers. And we asked for internal tangents so
they will not meet away from the circles.

They meet in between them

CONSTRUCTION OF ELLIPSE – 1

1.Which of the following is incorrect about
Ellipse?
a) Eccentricity is less than 1
b) Mathematical equation is X² /a² + Y²/b² =1
c) If a plane is parallel to axis of cone cuts the
cone then the section gives ellipse
d) The sum of the distances from two focuses
and any point on the ellipse is constant
Answer: c
Explanation: If a plane is parallel to the axis
of cone cuts the cone then the cross-section
gives hyperbola. If the plane is parallel to
base it gives circle. If the plane is inclined
with an angle more than the external angle of
cone it gives parabola. If the plane is inclined
and cut every generators then it forms an
ellipse.
2.Which of the following constructions
doesn’t use elliptical curves?
a) Cooling towers
b) Dams
c) Bridges
d) Man-holes
Answer: a
Explanation: Cooling towers, water channels use Hyperbolic curves as their design, Arches, Bridges, sound reflectors, lighter flectors etc use parabolic curves. Arches, bridges, dams, monuments, man-holes, glandsbridges, dams, monuments, man-holes, glands and stuffing boxes etc use elliptical curves.

3.The line which passes through the focus
and perpendicular to the major axis is
a) Minor axis
b) Latus rectum
c) Directrix
d) Tangent
Answer: b
Explanation: The line bisecting the major
axis at right angles and terminated by curve is
called the minor axis. The line which passes
through the focus and perpendicular to the
major axis is latus rectum. Tangent is the line
which touches the curve at only one point.
4.Which of the following is the eccentricity
for an ellipse?
a) 1
b) 3/2
c) 2/3
d) 5/2
Answer: c
Explanation: The eccentricity for ellipse is
always less than 1. The eccentricity is always
1 for any parabola. The eccentricity is always
0 for a circle. The eccentricity for a hyperbola
is always greater than 1.
5.Axes are called conjugate axes when they
are parallel to the tangents drawn at their
extremes.
a) True
b) False
Answer: a
Explanation: In ellipse there exist two axes
(major and minor) which are perpendicular to
each other, whose extremes have tangents
parallel them. There exist two conjugate axes
for ellipse and 1 for parabola and hyperbola.
6.Steps are given to draw an ellipse by loop
of the thread method. Arrange the steps.
i. Check whether the length of the thread is
enough to touch the end of minor axis.
ii. Draw two axes AB and CD intersecting at
O. Locate the foci F1 and F2.
iii. Move the pencil around the foci,
maintaining an even tension in the thread
throughout and obtain the ellipse.
iv. Insert a pin at each focus-point and tie a
piece of thread in the form of a loop around
the pins.
a) i, ii, iii, iv
b) ii, iv, i, iii
c) iii, iv, i, ii
d) iv, i, ii, iii
Answer: b
Explanation: This is the easiest method of
drawing ellipse if we know the distance
between the foci and minor axis, major axis.
It is possible since ellipse can be traced by a
point, moving in the same plane as and in
such a way that the sum of its distances from
two foci is always the same.
7.Steps are given to draw an ellipse by
trammel method. Arrange the steps.
i. Place the trammel so that R is on the minor
axis CD and Q on the major axis AB. Then P
will be on the ellipse.
ii. Draw two axes AB and CD intersecting
each other at O.
iii. By moving the trammel to new positions,
always keeping R on CD and Q on AB,
obtain other points and join those to get an
ellipse.
iv. Along the edge of a strip of paper which
may be used as a trammel, mark PQ equal to
half the minor axis and PR equal to half of
major axis.
a) i, ii, iii, iv
b) ii, iv, i, iii
c) iii, iv, i, ii
d) iv, i, ii, iii
Answer: b
Explanation: This method uses the trammels PQ and PR which ends Q and R should be placed on major axis and minor axis respectively. It is possible since ellipse can be traced by a point, moving in the same plane as and in such a way that the sum of its distances from two foci is always the same.

8.Steps are given to draw a normal and a
tangent to the ellipse at a point Q on it.
Arrange the steps.
i. Draw a line ST through Q and
perpendicular to NM.
ii. ST is the required tangent.
iii. Join Q with the foci F1 and F2.
iv. Draw a line NM bisecting the angle
between the lines drawn before which is
normal.
a) i, ii, iii, iv
b) ii, iv, i, iii
c) iii, iv, i, ii
d) iv, i, ii, iii
Answer: c
Explanation: Tangents are the lines which
touch the curves at only one point. Normals
are perpendiculars of tangents. As in the
circles first, we found the normal using foci
(centre in circle) and then perpendicular at
given point gives tangent.
9.Which of the following is not belonged to
ellipse?
a) Latus rectum
b) Directrix
c) Major axis
d) Asymptotes
Answer: d
Explanation: Latus rectum is the line joining
one of the foci and perpendicular to the major
axis. Asymptotes are the tangents which meet
the hyperbola at infinite distance. Major axis
consists of foci and perpendicular to the
minor axis.

CONSTRUCTION OF ELLIPSE – 2

1.Mathematically, what is the equation of
ellipse?
a) x²/a² + y²/b² = -1
b) x²/a²– y²/b² = 1
c) x²/a² + y²/b² = 1
d) x²/a²– y²/b² = 1
Answer: c
Explanation: Equation of ellipse is given by;
x²/a² + y²/b² = 1. Here, a and b are half the
distance of lengths of major and minor axes
of the ellipse. If the value of a = b then the
resulting ellipse will be a circle with Centre
(0,0) and radius equal to a units.
2.In general method of drawing an ellipse, a
vertical line called as is drawn first.
a) Tangent
b) Normal
c) Major axis
d) Directrix
Answer: d
Explanation: In the general method of
drawing an ellipse, a vertical line called as
directrix is drawn first. The focus is drawn at
a given distance from the directrix drawn.
The eccentricity of the ellipse is less than one.
3.If eccentricity of ellipse is 3/7, how many
divisions will the line joining the directrix
and the focus have in general method?
a) 10
b) 7
c) 3
d) 5
Answer: a
Explanation: In the general method of
drawing an ellipse, if eccentricity of the
ellipse is given as 3/7 then the line joining the
directrix and the focus will have 10 divisions.
The number is derived by adding the
numerator and denominator of the
eccentricity

4.In the general method of drawing an
ellipse, after parting the line joining the
directrix and the focus, a is made.
a) Tangent
b) Vertex
c) Perpendicular bisector
d) Normal
Answer: b
Explanation: In the general method of
drawing after parting the line joining the
directrix and the focus, a vertex is made. An
arc with a radius equal to the length between
the vertex and the focus is drawn with the
vertex as the centre.
5.An ellipse is defined as a curve traced by a
point which has the sum of distances between
any two fixed points always same in the same
plane.
a) True
b) False
Answer: a
Explanation: An ellipse can also be defined
as a curve that can be traced by a point
moving in the same plane with the sum of the
distances between any two fixed points
always same. The two fixed points are called
as a focus.
6.An ellipse has foci.
a) 1
b) 2
c) 3
d) 4
Answer: b
Explanation: An ellipse has 2 foci. These
foci are fixed in a plane. The sum of the
distances of a point with the foci is always
same. The ellipse can also be defined as the
curved traced by the points which exhibit this
property.
7.If information about the major and minor
axes of ellipse is given then by how many
methods can we draw the ellipse?
a) 2
b) 3
c) 4
d) 5
Answer: d
Explanation: There are 5 methods by which
we can draw an ellipse if we know the major
and minor axes of that ellipse. Those five
methods are arcs of circles method,
concentric circles method, loop of the thread
method, oblong method, trammel method.
8.In arcs of circles method, the foci are
constructed by drawing arcs with centre as
one of the ends of the axis and the
radius equal to the half of the axis.
a) Minor, major
b) Major, major
c) Minor, minor
d) Major, minor
Answer: a
Explanation: In arcs of circles method, the
foci are constructed by drawing arcs with
centre as one of the ends of the minor axis
and the radius equal to the half of the major
axis. This method is used when we know only
major and minor axes of the ellipse.
9.If we know the major and minor axes of
the ellipse, the first step of drawing the
ellipse, we draw the axes each other.
a) Parallel to
b) Perpendicular bisecting
c) Just touching
d) Coinciding
Answer: b
Explanation: If we know the major and
minor axes of the ellipse, the first step of the
drawing the ellipse is to draw the major and
minor axes perpendicular bisecting each
other. The major and the minor axes are
perpendicular bisectors of each other.

10.Loop of the thread method is the practical
application of method.

a) Oblong method
b) Trammel method
c) Arcs of circles method
d) Concentric method
Answer: c
Explanation: Loop of the thread method is
the practical application of the arcs of circles
method. The lengths of the ends of the minor
axis are half of the length of the major axis.
In this method, a pin is inserted at the foci
point and the thread is tied to a pencil which
is used to draw the curve.

CONSTRUCTION OF PARABOLA

1.Which of the following is incorrect about
Parabola?
a) Eccentricity is less than 1
b) Mathematical equation is x² = 4ay
c) Length of latus rectum is 4a
d) The distance from the focus to a vertex is
equal to the perpendicular distance from a
vertex to the directrix
Answer: a
Explanation: The eccentricity is equal to one.
That is the ratio of a perpendicular distance
from point on curve to directrix is equal to
distance from point to focus. The eccentricity
is less than 1 for an ellipse, greater than one
for hyperbola, zero for a circle, one for a
parabola.
2.Which of the following constructions use
parabolic curves?
a) Cooling towers
b) Water channels
c) Light reflectors
d) Man-holes
Answer: c
Explanation: Arches, Bridges, sound
reflectors, light reflectors etc use parabolic
curves. Cooling towers, water channels use
Hyperbolic curves as their design. Arches,
bridges, dams, monuments, man-holes, glands
and stuffing boxes etc use elliptical curves.
3.The length of the latus rectum of the
parabola y² =ax is
a) 4a
b) a
c) a/4
d) 2a
Answer: b
Explanation: Latus rectum is the line
perpendicular to axis and passing through
focus ends touching parabola. Length of latus
rectum of y² =4ax, x² =4ay is 4a; y² =2ax, x²=2ay is 2a; y² =ax, x² =ay is a.
4.Which of the following is not a parabola
equation?
a) x² = 4ay
b) y²– 8ax = 0
c) x² = by
d) x² = 4ay²
Answer: d
Explanation: The remaining represents
different forms of parabola just by adjusting
them we can get general notation of parabola
but x² = 4ay² gives equation for hyperbola.
And x² + 4ay² =1 gives equation for ellipse.
5.The parabola x2 = ay is symmetric about x-axis.
a) True
b) False
Answer: b
Explanation: From the given parabolic
equation x² = ay we can easily say if we give
y values to that equation we get two values
for x so the given parabola is symmetric
about y-axis. If the equation is y² = ax then it
is symmetric about x-axis.

6.Steps are given to find the axis of a
parabola. Arrange the steps.

i. Draw a perpendicular GH to EF which cuts
parabola.
ii. Draw AB and CD parallel chords to given
parabola at some distance apart from each
other.
iii. The perpendicular bisector of GH gives
axis of that parabola.
iv. Draw a line EF joining the midpoints lo
AB and CD.
a) i, ii, iii, iv
b) ii, iv, i, iii
c) iii, iv, i, ii
d) iv, i, ii, iii
Answer: b
Explanation: First we drawn the parallel
chords and then line joining the midpoints of
the previous lines which is parallel to axis so
we drawn the perpendicular to this line and
then perpendicular bisector gives the axis of
parabola.

7.Steps are given to find focus for a parabola.
Arrange the steps.
i. Draw a perpendicular bisector EF to BP,
Intersecting the axis at a point F.
ii. Then F is the focus of parabola.
iii. Mark any point P on the parabola and
draw a perpendicular PA to the axis.
iv. Mark a point B on the on the axis such that
BV = VA (V is vertex of parabola). Join B
and P.
a) i, ii, iii, iv
b) ii, iv, i, iii
c) iii, iv, i, ii
d) iv, i, ii, iii
Answer: c
Explanation: Initially we took a parabola
with axis took any point on it drawn a
perpendicular to axis. And from the point
perpendicular meets the axis another point is
taken such that the vertex is equidistant from
before point and later point. Then from that
one to point on parabola a line is drawn and
perpendicular bisector for that line meets the
axis at focus.
8.Which of the following is not belonged to
ellipse?
a) Latus rectum
b) Directrix
c) Major axis
d) Axis
Answer: c
Explanation: Latus rectum is the line joining
one of the foci and perpendicular to the major
axis. Major axis and minor axis are in ellipse
but in parabola, only one focus and one axis
exist since eccentricity is equal to 1.

CONSTRUCTION OF HYPERBOLA

1.Which of the following is Hyperbola
equation?
a) y² + x²/b² = 1
b) x²= 1ay
c)x² /a²– y²/b² = 1
d) x² + y² = 1
Answer: c
Explanation: The equation x²+ y² = 1 gives
a circle; if the x² and y² have same co-efficient then the equation gives circles. The
equation x²= 1ay gives a parabola. The
equation y² + x²/b² = 1 gives an ellipse.
2.Which of the following constructions use
hyperbolic curves?
a) Cooling towers
b) Dams
c) Bridges
d) Man-holes
Answer: a
Explanation: Cooling towers, water channels
use Hyperbolic curves as their design.
Arches, Bridges, sound reflectors, light
reflectors etc., use parabolic curves. Arches,
bridges, dams, monuments, man-holes, glands
and stuffing boxes etc., use elliptical curves.

3.The lines which touch the hyperbola at an
infinite distance are
a) Axes
b) Tangents at vertex
c) Latus rectum
d) Asymptotes
Answer: d
Explanation: Axis is a line passing through
the focuses of a hyperbola. The line which
passes through the focus and perpendicular to
the major axis is latus rectum. Tangent is the
line which touches the curve at only one
point.
4.Which of the following is the eccentricity
for hyperbola?
a) 1
b) 3/2
c) 2/3
d) 1/2
Answer: b
Explanation: The eccentricity for an ellipse
is always less than 1. The eccentricity is
always 1 for any parabola. The eccentricity is
always 0 for a circle. The eccentricity for a
hyperbola is always greater than 1.
5.If the asymptotes are perpendicular to each
other then the hyperbola is called rectangular
hyperbola.
a) True
b) False
Answer: a
Explanation: In ellipse there exist two axes
(major and minor) which are perpendicular to
each other, whose extremes have tangents
parallel them. There exist two conjugate axes
for ellipse and 1 for parabola and hyperbola.
6.A straight line parallel to asymptote
intersects the hyperbola at only one point.
a) True
b) False
Answer: a
Explanation: A straight line parallel to
asymptote intersects the hyperbola at only
one point. This says that the part of hyperbola
will lay in between the parallel lines through
outs its length after intersecting at one point.
7.Steps are given to locate the directrix of
hyperbola when axis and foci are given.
Arrange the steps.
i. Draw a line joining A with the other Focus
F.
ii. Draw the bisector of angle FAF1, cutting
the axis at a point B.
iii. Perpendicular to axis at B gives directrix.
iv. From the first focus F1 draw a
perpendicular to touch hyperbola at A.
a) i, ii, iii, iv
b) ii, iv, i, iii
c) iii, iv, i, ii
d) iv, i, ii, iii
Answer: d
Explanation: The directrix cut the axis at the
point of intersection of the angular bisector of
lines passing through the foci and any point
on a hyperbola. Just by knowing this we can
find the directrix just by drawing
perpendicular at that point to axis.
8.Steps are given to locate asymptotes of
hyperbola if its axis and focus are given.
Arrange the steps.
i. Draw a perpendicular AB to axis at vertex.
ii. OG and OE are required asymptotes.
iii. With O midpoint of axis (centre) taking
radius as OF (F is focus) draw arcs cutting
AB at E, G.
iv.Join O, G and O, E.
a) i, iii, iv, ii
b) ii, iv, i, iii
c) iii, iv, i, ii
d) iv, i, ii, iii
Answer: b
Explanation: Asymptotes pass through centre is the main point and then the asymptotes cut the directrix and perpendiculars at focus are known and simple. Next comes is where the asymptotes cuts the perpendiculars, it is at distance of centre to vertex and centre to focus respectively.

9.The asymptotes of any hyperbola intersects at
a) On the directrix
b) On the axis
c) At focus
d) Centre
Answer: d
Explanation: The asymptotes intersect at
centre that is a midpoint of axis even for
conjugate axis it is valid. Along with the
hyperbola asymptotes are also symmetric
about both axes so they should meet at centre
only.

CONSTRUCTION OF CYCLOIDAL CURVES

1.Is a curve generated by a
point fixed to a circle, within or outside its
circumference, as the circle rolls along a
straight line.
a) Cycloid
b) Epicycloid
c) Epitrochoid
d) Trochoid
Answer: d
Explanation: Cycloid form if generating
point is on the circumference of generating a
circle. Epicycloid represents generating circle
rolls on the directing circle. Epitrochoid is
that the generating point is within or outside
the generating circle but generating circle
rolls on directing circle.
2.Is a curve generated by a
point on the circumference of a circle, which
rolls without slipping along another circle
outside it.
a) Trochoid
b) Epicycloid
c) Hypotrochoid
d) Involute
Answer: b
Explanation: Trochoid is curve generated by
a point fixed to a circle, within or outside its
circumference, as the circle rolls along a
straight line. ‘Hypo’ represents the generating
circle is inside the directing circle.
3.Is a curve generated by a point
on the circumference of a circle which rolls
without slipping on a straight line.
a) Trochoid
b) Epicycloid
c) Cycloid
d) Evolute
Answer: c
Explanation: Trochoid is curve generated by
a point fixed to a circle, within or outside its
circumference, as the circle rolls along a
straight line. Cycloid is a curve generated by
a point on the circumference of a circle which
rolls along a straight line. ‘Epi’ represents the
directing path is a circle.
4.When the circle rolls along another circle
inside it, the curve is called a
a) Epicycloid
b) Cycloid
c) Trochoid
d) Hypocycloid
Answer: d
Explanation: Cycloid is a curve generated by
a point on the circumference of a circle which
rolls along a straight line. ‘Epi’ represents the
directing path is a circle. Trochoid is a curve
generated by a point fixed to a circle, within
or outside its circumference, as the circle rolls
along a straight line. ‘Hypo’ represents the
generating circle is inside the directing circle.

6.Match the following
Generating point is – i. Inferior within the circumference trochoid

Generating point is on the circumference of circle and – ii. Epicycloid generating circle rolls on
straight line.

The circumference of circle and generating circle rolls on straight line – iii. Cycloid

Generating point is on the circumference of circle

and generating circle rolls – iv. Superior
trochoid

a) 1, i; 2, iii; 3, iv; 4, ii
b) 1, ii; 2, iii; 3, i; 4, iv
c) 1, ii; 2, iv; 3, iii; 4, i
d) 1, iv; 2, iii; 3, ii; 4, i
Answer: a

Explanation: Trochoid is curve generated by
a point fixed to a circle, within or outside its
circumference, as the circle rolls along a
straight line. Inferior or superior depends on
whether the generating point in within or
outside the generating circle. If directing path
is straight line then the curve is cycloid.

7.Steps are given to find the normal and
tangent for a cycloid. Arrange the steps if C is
the centre for generating circle and PA is the
directing line. N is the point on cycloid.
i. Through M, draw a line MO perpendicular
to the directing line PA and cutting at O.
ii. With centre N and radius equal to radius of
generating circle, draw an arc cutting locus of
C at M.

iii. Draw a perpendicular to ON at N which is tangent.

iv. Draw a line joining O and N which is
normal.

a) iii, i, iv, ii
b) ii, i, iv, iii
c) iv, ii, i, iii
d) i, iv, iii, ii
Answer: b
Explanation: The normal at any point on a cycloidal curve will pass through the corresponding point of contact between the generating circle and the directing line. So with help of locus of centre of generating circle we found the normal and the tangent.

8.Steps are given to find the normal and
tangent to an epicycloid. Arrange the steps if
C is the centre for generating circle and O is
the centre of directing cycle. N is the point on
epicycloid.
i. Draw a line through O and D cutting
directing circle at M.
ii. Draw perpendicular to MN at N. We get
tangent.
iii. With centre N and radius equal to radius
of generating circle, draw an arc cutting the
locus of C at D.
iv. Draw a line joining M and N which is
normal.
a) iii, i, iv, ii
b) ii, i, iv, iii
c) iv, ii, i, iii
d) i, iv, iii, ii
Answer: a
Explanation: The normal at any point on an
epicycloidal curve will pass through the
corresponding point of contact between the
generating circle and the directing circle. And
also with help of locus of centre of generating
circle we found the normal and the tangent.
9.The generating circle will be inside the
directing circle for
a) Cycloid
b) Inferior trochoid
c) Inferior epitrochoid
d) Hypocycloid
Answer: d
Explanation: The generating circle will be
inside the directing circle for hypocycloid or
hypotrochoid. Trochoid is a curve generated
by a point fixed to a circle, within or outside
its circumference, as the circle rolls along a
straight line or over circle if not represented
with hypo as a prefix.
10.The generating point is outside the
generating circle for
a) Cycloid
b) Superior Trochoid
c) Inferior Trochoid
d) Epicycloid
Answer: b
Explanation: If the generating point is on the
circumference of generating circle then the
curve formed may be cycloids or
hypocycloids. Trochoid is a curve generated
by a point fixed to a circle, within or outside
its circumference, as the circle rolls along a
straight line or a circle. But here given is
outside so it is superior trochoid.

CONSTRUCTION OF INVOLUTE

1.Mathematical equation for Involute is
a) x = a cos3θ
b) x = r cosθ + r θ sinθ
c) x = (a+b)cosθ – a cos(a+b⁄a θ)
d) y = a(1-cosθ)
Answer: b
Explanation: x= a cos3 Ɵ is equation forhypocycloid, x= (a+ b) cosƟ – a cos ((a+b)/aƟ) is equation for epicycloid, y= a (1-cosƟ) is equation for cycloid and x = r cosƟ r Ɵ sinƟ is equation for Involute.

2.Steps are given to draw involute of given
circle. Arrange the steps f C is the centre of
circle and P be the end of the thread (starting
point).
i. Draw a line PQ, tangent to the circle and
equal to the circumference of the circle.
ii. Draw the involute through the points P1,
P2, P3 ……….etc.
iii. Divide PQ and the circle into 12 equal
parts.
iv. Draw tangents at points 1, 2, 3 etc. and
mark on them points P1, P2, P3 etc. such that
1P1 =P1l, 2P2 = P2l, 3P3= P3l etc.
a) ii, i, iv, iii

b) iii, i , iv, ii
c) i, iii, iv, ii
d) iv, iii, i, ii
Answer: c
Explanation: Involute is a curve which is
formed by the thread which is yet complete a
single wound around a circular object so thus
the thread having length equal to the
circumference of the circular object. And the
involute curve follows only the thread is kept
straight while wounding.

3.Steps are given to draw tangent and normal
to the involute of a circle (center is C) at a
point N on it. Arrange the steps.
i. With CN as diameter describe a semi-circle
cutting the circle at M.
ii. Draw a line joining C and N.
iii. Draw a line perpendicular to NM and
passing through N which is tangent.
iv. Draw a line through N and M. This line is
normal.
a) ii, i, iv, iii
b) iii, i , iv, ii
c) i, iii, iv, ii
d) iv, iii, i, ii
Answer: a
Explanation: The normal to an involute of a
circle is tangent to that circle. So simply by
finding the appreciable tangent of circle
passing through the point given on involute
gives the normal and then by drawing
perpendicular we can find the tangent to
involute.
4.Steps given are to draw an involute of a
given square ABCD. Arrange the steps.
i. With B as centre and radius BP1 (BA+ AD)
draw an arc to cut the line CB-produced at
P2.
ii. The curve thus obtained is the involute of
the square.
iii. With centre A and radius AD, draw an arc
to cut the line BA-produced at a point P1.
iv. Similarly, with centres C and D and radii
CP2 and DP3 respectively, draw arcs to cut
DC-produced at P3 and AD-produced at P4.
a) ii, i, iv, iii
b) iii, i , iv, ii
c) i, iii, iv, ii
d) iv, iii, i, ii
Answer: b
Explanation: It is easy to draw involutes to
polygons. First, we have to point the initial
point and then extending the sides. Then
cutting the extended lines with cumulative
radiuses of length of sides gives the points on
involute and then joining them gives involute.
5.Steps given are to draw an involute of a
given triangle ABC. Arrange the steps.
i. With C as centre and radius C1 draw arc
cutting AC-extended at 2.
ii. With A as center and radius A2 draw an
arc cutting BA- extended at 3 completing
involute.
iii. B as centre with radius AB draw an arc
cutting the BC- extended at 1.
iv. Draw the given triangle with corners A, B, C.
a) ii, i, iv, iii
b) iii, i , iv, ii
c) i, iii, iv, ii
d) iv, iii, i, ii
Answer: d
Explanation: It will take few simple steps to
draw involute for a triangle since it has only 3
sides. First, we have to point the initial point
and then extending the sides. Then cutting the
extended lines with cumulative radiuses of
length of sides gives the points on involute
and then joining them gives involute.
6.Steps given are to draw an involute of a
given pentagon ABCDE. Arrange the steps.
i. B as centre and radius AB, draw an arc
cutting BC –extended at 1.
ii. The curve thus obtained is the involute of
the pentagon.
iii. C as centre and radius C1, draw an arc
cutting CD extended at 2.
iv. Similarly, D, E, A as centres and radiusD2, E3, A4, draw arcs cutting DE, EA, AB at 3, 4, 5 respectively.

a) ii, i, iv, iii
b) iii, i , iv, ii
c) i, iii, iv, ii
d) iv, iii, i, ii
Answer: c
Explanation: It is easy to draw involutes to
polygons. First, we have to point the initial
point and then extending the sides. Then
cutting the extended lines with cumulative
radiuses of length of sides gives the points on
involute and then joining them gives involute.

7.For inferior trochoid or inferior epitrochoid
the curve touches the directing line or
directing circle.
a) True
b) False
Answer: b
Explanation: Since in the inferior trochoids
the generating point is inside the generating
circle the path will be at a distance from
directing line or circle even if the generating
circle is inside or outside the directing circle.
8.‘Hypo’ as prefix to cycloids give that the
generating circle is inside the directing circle.
a) True
b) False
Answer: a
Explanation: ‘Hypo’ represents the
generating circle is inside the directing circle.
‘Epi’ represents the directing path is a circle.
Trochoid represents the generating point is
not on the circumference of generating a
circle.

CONSTRUCTION OF SPIRAL

1.Which of the following represents an
Archemedian spiral?
a) Tornado
b) Cyclone
c) Mosquito coil
d) Fibonacci series
Answer: c
Explanation: Archemedian spiral is a curve
traced out by a point moving in such a way
that its movement towards or away from the
pole is uniform with the increase of the
vectorial angle from the starting line. It is
generally used for teeth profiles of helical
gears etc.
2.Steps are given to draw normal and tangent
to an archemedian curve. Arrange the steps, if
O is the center of curve and N is point on it.
i. Through N, draw a line ST perpendicular to
NM. ST is the tangent to the spiral.
ii. Draw a line OM equal in length to the
constant of the curve and perpendicular to
NO.
iii. Draw the line NM which is normal to the
spiral.
iv. Draw a line passing through the N and O
which is radius vector.
a) ii, iv, i, iii
b) i, iv, iii, ii
c) iv, ii, iii, i
d) iii, i, iv, ii
Answer: c
Explanation: The normal to an archemedian
spiral at any point is the hypotenuse of the
right angled triangle having the other two
sides equal in length to the radius vector at
that point and the constant of the curve
respectively.
3.Which of the following does not represents
an Archemedian spiral?
a) Coils in heater
b) Tendrils
c) Spring
d) Cyclone
Answer: d
Explanation: Tendrils are a slender thread-like structures of a climbing plant, often growing in a spiral form. For cyclones the moving point won’t have constant velocity. The archemedian spirals have a constant increase in the length of a moving point. Spring is a helix.
4.Logarithmic spiral is also called
Equiangular spiral.
a) True
b) False
Answer: a
Explanation: The logarithmic spiral is also
known as equiangular spiral because of its
property that the angle which the tangent at
any point on the curve makes with the radius
vector at that point is constant. The values of
vectorial angles are in arithmetical
progression.
In logarithmic Spiral, the radius vectors are
in arithmetical progression.
a) True
b) False
Answer: b
Explanation: In the logarithmic Spiral, the
values of vectorial angles are in arithmetical
progression and radius vectors are in the
geometrical progression that is the lengths of
consecutive radius vectors enclosing equal
angles are always constant.
The mosquito coil we generally see in
house hold purposes and heating coils in
electrical heater etc are generally which
spiral.
a) Logarithmic spiral
b) Equiangular spiral
c) Fibonacci spiral
d) Archemedian spiral
Answer: d
Explanation: Archemedian spiral is a curve
traced out by a point moving in such a way
that its movement towards or away from the
pole is uniform with the increase of the
vectorial angle from the starting line. The use
of this curve is made in teeth profiles of
helical gears, profiles of cam etc.

BASICS OF CONIC SECTIONS – 1

1.The sections cut by a plane on a right
circular cone are called as
a) Parabolic sections
b) Conic sections
c) Elliptical sections
d) Hyperbolic sections
Answer: b
Explanation: The sections cut by a plane on a
right circular cone are called as conic sections
or conics. The plane cuts the cone on
different angles with respect to the axis of the
cone to produce different conic sections.
2.Which of the following is a conic section?
a) Circle
b) Rectangle
c) Triangle
d) Square
Answer: a
Explanation: Circle is a conic section. When
the plane cuts the right circular cone at right
angles with the axis of the cone, the shape
obtained is called as a circle. If the angle is
oblique we get the other parts of the conic
sections.
3.In conics, the is revolving to form
two anti-parallel cones joined at the apex.
a) Ellipse
b) Circle
c) Generator
d) Parabola
Answer: c
Explanation: In conics, the generator is
revolving to form two anti-parallel cones
joined at the apex. The plane is then made to
cut these cones and we get different conic
sections. If we cut at right angles with respect
to the axis of the cone we get a circle.
4.While cutting, if the plane is at an angle
and it cuts all the generators, then the conic
formed is called as
a) Circle
b) Ellipse
c) Parabola
d) Hyperbola
Answer: b
Explanation: If the plane cuts all the
generators and is at an angle to the axis of the
cone, then the resulting conic section is called
as an ellipse. If the cutting angle was right
angle and the plane cuts all the generators
then the conic formed would be circle.

5.If the plane cuts at an angle to the axis but
does not cut all the generators then what is
the name of the conics formed?

a) Ellipse
b) Hyperbola
c) Circle
d) Parabola
Answer: d
Explanation: If the plane cuts at an angle
with respect to the axis and does not cut all
the generators then the conics formed is a
parabola. If the plane cuts all the generators
then the conic section formed is called as
ellipse.

6.When the plane cuts the cone at angle
parallel to the axis of the cone, then is
formed.
a) Hyperbola
b) Parabola
c) Circle
d) Ellipse
Answer: a
Explanation: When the plane cuts the cone at
an angle parallel to the axis of the cone, then
the resulting conic section is called as a
hyperbola. If the plane cuts the cone at an
angle with respect to the axis of the cone then
the resulting conic sections are called as
ellipse and parabola.
7.Which of the following is not a conic
section?
a) Apex
b) Hyperbola
c) Ellipse
d) Parabola
Answer: a
Explanation: Conic sections are formed
when a plane cuts through the cone at an
angle with respect to the axis of the cone. If
the angle is right angle then the conics is a
circle, if the angle is oblique then the
resulting conics are parabola and ellipse.
8.The locus of point moving in a plane such
that the distance between a fixed point and a
fixed straight line is constant is called as
a) Conic
b) Rectangle
c) Square
d) Polygon
Answer: a
Explanation: The locus of a point moving in
a plane such that the distance between a fixed
point and a fixed straight line is always
constant. The fixed straight line is called as
directrix and the fixed point is called as the
focus.
9.The ratio of the distance from the focus to
the distance from the directrix is called as
eccentricity.
a) True
b) False
Answer: a
Explanation: The ratio of the distance from
the focus to the distance from the directrix is
called eccentricity. It is denoted as e. The
value of eccentricity can give information
regarding which type of conics it is.
10.Which of the following conics has an
eccentricity of unity?
a) Circle
b) Parabola
c) Hyperbola
d) Ellipse
Answer: b
Explanation: Eccentricity is defined as the
ratio of the distance from the focus to the
distance from the directrix. It is denoted as e.
The value of eccentricity can give
information regarding which type of conics it
is. The eccentricity of a parabola is the unity
that is 1.
Which of the following has an
eccentricity less than one?
a) Circle
b) Parabola

c) Hyperbola
d) Ellipse
Answer: d
Explanation: Eccentricity is defined as the
ratio of the distance from the focus to the
distance from the directrix. It is denoted as e.
The value of eccentricity can give
information regarding which type of conics it
is. The eccentricity of an ellipse is less than
one.

12.If the distance from the focus is 10 units
and the distance from the directrix is 30 units,
then what is the eccentricity?
a) 0.3333
b) 0.8333
c) 1.6667
d) 0.0333
Answer: a
Explanation: Eccentricity is defined as the
ratio of the distance from the focus to the
distance from the directrix. Hence from the
formula of eccentricity, e = 10 ÷ 30 = 0.3333.
Since the value of eccentricity is less than one
the conic is an ellipse.
13.If the value of eccentricity is 12, then
what is the name of the conic?
a) Ellipse
b) Hyperbola
c) Parabola
d) Circle
Answer: b
Explanation: Eccentricity is defined as the
ration of the distance from the focus to the
distance from the directrix. It is denoted as e.
If the value of eccentricity is greater than
unity then the conic section is called as a
hyperbola.
14.If the distance from the focus is 3 units
and the distance from the directrix is 3 units,
then how much is the eccentricity?
a) Infinity
b) Zero
c) Unity
d) Less than one
Answer: c
Explanation: Eccentricity is defined as the
ration of the distance from the focus to the
distance from the directrix and it is denoted as
e. Hence from the definition, e = 3 ÷ 3 = 1.
Hence the value of eccentricity is equal to
unity.
15.If the distance from the focus is 2 mm and
the distance from the directrix is 0.5 mm then
what is the name of the conic section?
a) Circle
b) Ellipse
c) Parabola
d) Hyperbola
Answer: d
Explanation: The eccentricity is defined as
the ratio of the distance from the focus to the
distance from the directrix. It is denoted as e.
If the value of the eccentricity is greater than
unity then the conic section is called as a
hyperbola.

BASICS OF CONIC SECTIONS – 2

1.Which of the following is a conic section?
a) Apex
b) Circle
c) Rectangle
d) Square
Answer: b
Explanation: Conic sections are formed
when a plane cuts through the cone at an
angle with respect to the axis of the cone. If
the angle is right angle then the conics is a
circle, if the angle is oblique then the
resulting conics are parabola and ellipse.
2.Which of the following has an eccentricity
more than unity?
a) Parabola

b) Circle
c) Hyperbola
d) Ellipse
Answer: c
Explanation: Eccentricity is defined as the
ratio of the distance from the focus to the
distance from the directrix. It is denoted as e.
The value of eccentricity can give
information regarding which type of conics it
is. The eccentricity of a hyperbola is more
than one.

3.If the distance from the focus is 10 units
and the distance from the directrix is 30 units,
then what is the name of the conic?
a) Circle
b) Parabola
c) Hyperbola
d) Ellipse
Answer: d
Explanation: Eccentricity is defined as the
ratio of the distance from the focus to the
distance from the directrix. Hence from the
formula of eccentricity, e = 10 ÷ 30 = 0.3333.
Since the value of eccentricity is less than one
the conic is an ellipse.
4.If the distance from the focus is 2 mm and
the distance from the directrix is 0.5 mm then
what is the value of eccentricity?
a) 0.4
b) 4
c) 0.04
d) 40
Answer: b
Explanation: Eccentricity is defined as the
ratio of the distance from the focus to the
distance from the directrix and it is denoted
by e. Therefore, by definition, e = 2 ÷ 0.5 = 4.
Hence the conic section is called as
hyperbola.
5.If the distance from the focus is 3 units and
the distance from the directrix is 3 units, then
what is the name of the conic section?
a) Ellipse
b) Hyperbola
c) Circle
d) Parabola
Answer: d
Explanation: Eccentricity is defined as the
ratio of the distance from the focus to the
distance from the directrix and it is denoted
by e. Therefore, by definition, e = 3 ÷ 3 = 1.
Hence the conic section is called as a
parabola.
6.If the distance from the directrix is 5 units
and the distance from the focus is 3 units then
what is the name of the conic section?
a) Ellipse
b) Parabola
c) Hyperbola
d) Circle
Answer: a
Explanation: Eccentricity is defined as the
ratio of the distance from the focus to the
distance from the directrix and it is denoted
by e. Hence, by definition, e = 3 ÷ 5 = 0.6.
Hence the conic section is called an ellipse.
7.If the distance from a fixed point is greater
than the distance from a fixed straight line
then what is the name of the conic section?
a) Parabola
b) Circle
c) Hyperbola
d) Ellipse
Answer: c
Explanation: The fixed point is called as
focus and the fixed straight line is called as
directrix. Eccentricity is defined as the ratio
of the distance from the focus to the distance
from the directrix and it is denoted by e. If e
is greater than one then the conic section is
called as a hyperbola.
8.If the distance from a fixed straight line is
equal to the distance from a fixed point then
what is the name of the conic section?

b) Parabola
c) Hyperbola
d) Circle
Answer: b
Explanation: The fixed straight line is called
as directrix and the fixed point is called as a
focus. Eccentricity is defined as the ratio of
the distance from the focus to the distance
from the directrix and it is denoted by e.
Eccentricity of a parabola is unity.

9.If the distance from the directrix is greater
than the distance from the focus then what is
the value of eccentricity?
a) Unity
b) Less than one
c) Greater than one
d) Zero
Answer: b
Explanation: Eccentricity is defined as the
ratio of the distance from the focus to the
distance from the directrix and it is denoted
by e. Therefore, by definition the value of
eccentricity is less than one hence the conic
section is an ellipse.
10.If the distance from the directrix is 5 units
and the distance from the focus is 3 units then
what is the value of eccentricity?
a) 1.667
b) 0.833
c) 0.60
d) 0.667
Answer: c
Explanation: Eccentricity is defined as the
ratio of the distance from the focus to the
distance from the directrix and it is denoted
by e. Therefore, by definition, e = 3 ÷ 5 = 0.6.
Hence the conic section is called an ellipse.
11.If the distance from a fixed straight line is
5mm and the distance from a fixed point is
14mm then what is the name of the conic
section?
a) Hyperbola
b) Parabola
c) Ellipse
d) Circle
Answer: a
Explanation: The fixed straight line is called
directrix and the fixed point is called as a
focus. Eccentricity is defined as the ratio of
the distance from the focus to the distance
from the directrix and it is denoted by e.
Hence from definition e = 14 ÷ 5 = 2.8. The
eccentricity of a hyperbola is greater than
one.
12.If the distance from the directrix is greater
than the distance from the focus then what is
the name of the conic section?
a) Hyperbola
b) Parabola
c) Ellipse
d) Circle
Answer: c
Explanation: Eccentricity is defined as the
ratio of the distance from the focus to the
distance from the directrix and it is denoted
by e. Therefore, by definition the value of
eccentricity is less than one hence the conic
section is an ellipse.
13.If the distance from a fixed straight line is
equal to the distance from a fixed point then
what is the value of eccentricity?
a) Unity
b) Greater than one
c) Infinity
d) Zero
Answer: a
Explanation: The fixed straight line is called
as directrix and the fixed point is called as a
focus. Eccentricity is defined as the ratio of
the distance from the focus to the distance
from the directrix and it is denoted by e.
Hence from definition e = x ÷ x = 1.

14.If the distance from a fixed point is
greater than the distance from a fixed straight
line then what is the value of eccentricity?
a) Unity
b) Infinity
c) Zero
d) Greater than one
Answer: d
Explanation: The fixed point is called as
focus and the fixed straight line is called as
directrix. Eccentricity is defined as the ratio
of the distance from the focus to the distance
from the directrix and it is denoted by e.
Hence from the definition, the value of
eccentricity is greater than one.
15.If the distance from a fixed straight line is
5mm and the distance from a fixed point is
14mm then what is the value of eccentricity?
a) 0.357
b) 3.57
c) 2.8
d) 0.28
Answer: c
Explanation: The fixed straight line is called
as directrix and the fixed point is called as a
focus. Eccentricity is defined as the ratio of
the distance from the focus to the distance
from the directrix and it is denoted by e.
Hence from definition e = 14 ÷ 5 = 2.8.

BASICS OF CONIC SECTIONS – 3

1.Choose the correct option.

(a)Eccentricity= Distance of the point from the focus/ Distance of the point from the vertex

(b)Eccentricity= Distance of the point from the focus/ Distance of the point from the directrix

(c)Eccentricity= Distance of the point from the directrix / Distance of the point from the focus

(d)Eccentricity= Distance of the point from the latus rectum/ Distance of the point from the focus

Answer: b
Explanation: The point where the extension
of major axis meets the curve is called vertex.
The conic is defined as the locus of a point in
such a way that the ratio of its distance from a
fixed point and a fixed straight line is always
constant. The ratio gives the eccentricity. The
fixed point is called the focus and the fixed
line is called directrix.

2. 2.Match the following.

A. E < 1 i. Rectangular hyperbola

B. E = 1 ii. Hyperbola

C. E > 1 iii. Ellipse

D. E > 1 iv. Parabola

a) A, i; B, ii; C, iii; D, iv

b) A, ii; B, iii; C, iv; D, i

c) A, iii; B, iv; C, ii; D, i

d) A, iv; B, iii; C, ii; D, i

Answer: c

Explanation: The conic is defined as the locus of a point in such a way that the ratio of its distance from a fixed point and a fixed straight line is always constant. The fixed point is called the focus and the fixed line is called directrix. The change in ratio as given above results in different curves.

3.A plane is parallel to a base of regular cone
and cuts at the middle. The cross-section is

a) Circle
b) Parabola
c) Hyperbola
d) Ellipse
Answer: a
Explanation: A cone is formed by reducing
the cross-section of a circle the point. So
there exist circles along the cone parallel to
the base. Since the given plane is parallel to
the base of the regular cone. The crosssection will be circle

4.The cross-section is a when a
plane is inclined to the axis and cuts all the
generators of a regular cone.
a) Rectangular Hyperbola
b) Hyperbola
c) Circle
d) Ellipse
Answer: d
Explanation: A cone is a solid or hollow
object which tapers from a circular base to a
point. Here given an inclined plane which
cuts all the generators of a regular cone. So
the cross-section will definitely ellipse.
5.The curve formed when eccentricity is
equal to one is
a) Parabola
b) Circle
c) Semi-circle
d) Hyperbola
Answer: a
Explanation: The answer is parabola. Circle
has an eccentricity of zero and semi circle is
part of circle and hyper eccentricity is greater
than one.

6.The cross-section gives a when the cutting plane is parallel to axis of cone.
a) Parabola
b) Hyperbola
c) Circle
d) Ellipse
Answer: b
Explanation: If the cutting plane makes angle
less than exterior angle of the cone the crosssection gives a ellipse. If the cutting plane
makes angle greater than the exterior angle of
the cone the cross- section may be parabola or
hyperbola.

7.A plane cuts the cylinder the plane is not
parallel to the base and cuts all the generators.
The Cross-section is
a) Circle
b) Ellipse
c) Parabola
d) Hyperbola
Answer: b
Explanation: Given is a plane which is
inclined but cutting all the generators so it
will be an ellipse. Cutting of all generators
gives us information that the cross-section
will be closed curve and not parabola or
hyperbola. Circle will form only if plane is
parallel to the base.
8.A plane cuts the cylinder and the plane is
parallel to the base and cuts all the generators.
The Cross-section is
a) Circle
b) Ellipse
c) Parabola
d) Rectangular hyperbola
Answer: a
Explanation: The plane which is parallel to base will definitely cut the cone at all generators. Here additional information also given that the plane is parallel to base so the cross-section will be circle.

9.The curve which has eccentricity zero is
a) Parabola
b) Ellipse
c) Hyperbola
d) Circle
Answer: d
Explanation: The eccentricity is the ratio of a
distance from a point on the curve to focus
and to distance from the point to directrix.
For parabola it is 1 and for ellipse it is less
than 1 and for hyperbola it is greater than 1.
And for circle it is zero.
10.Rectangular hyperbola is one of the
hyperbola but the asymptotes are
perpendicular in case of rectangular
hyperbola.
a) True
b) False
Answer: a
Explanation: Asymptotes are the tangents
which meet the curve hyperbola at infinite
distance. If the asymptotes are perpendicular
to each other then hyperbola takes the name
of a rectangular hyperbola.

Prabakaran S

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