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

1. Which of the following is Hyperbola equation?

a) y^{2} + x^{2}/b^{2} = 1

b) x^{2}= 1ay

c) x^{2} /a^{2} – y^{2}/b^{2} = 1

d) X^{2} + Y^{2} = 1

View Answer

Explanation: The equation x

^{2}+ y

^{2}= 1 gives a circle; if the x

^{2}and y

^{2}have same co-efficient then the equation gives circles. The equation x

^{2}= 1ay gives a parabola. The equation y

^{2}+ x

^{2}/b

^{2}= 1 gives an ellipse.

2. Which of the following constructions use hyperbolic 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 lines which touch the hyperbola at an infinite distance are ________

a) Axes

b) Tangents at vertex

c) Latus rectum

d) Asymptotes

View Answer

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

View Answer

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

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. A straight line parallel to asymptote intersects the hyperbola at only one point.

a) True

b) False

View Answer

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

View Answer

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

View Answer

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

View Answer

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.

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