This set of Engineering Drawing Multiple Choice Questions & Answers (MCQs) focuses on “Construction of Ellipse – 1”.

1. Which of the following is incorrect about Ellipse?

a) Eccentricity is less than 1

b) Mathematical equation is X^{2} /a^{2} + Y^{2}/b^{2} = 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

View Answer

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

View Answer

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 line which passes through the focus and perpendicular to the major axis is ________

a) Minor axis

b) Latus rectum

c) Directrix

d) Tangent

View Answer

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

View Answer

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

View Answer

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

View Answer

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

View Answer

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

View Answer

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

View Answer

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.

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