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

1. Which of the following is incorrect about Parabola?

a) Eccentricity is less than 1

b) Mathematical equation is x^{2} = 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

View Answer

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

View Answer

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

View Answer

Explanation: Latus rectum is the line perpendicular to axis and passing through focus ends touching parabola. Length of latus rectum of y

^{2}=4ax, x

^{2}=4ay is 4a; y

^{2}=2ax, x

^{2}=2ay is 2a; y

^{2}=ax, x

^{2}=ay is a.

4. Which of the following is not a parabola equation?

a) x^{2} = 4ay

b) y^{2} – 8ax = 0

c) x^{2} = by

d) x^{2} = 4ay^{2}

View Answer

Explanation: The remaining represents different forms of parabola just by adjusting them we can get general notation of parabola but x

^{2}= 4ay

^{2}gives equation for hyperbola. And x

^{2}+ 4ay

^{2}=1 gives equation for ellipse.

5. The parabola x^{2} = ay is symmetric about x-axis.

a) True

b) False

View Answer

Explanation: From the given parabolic equation x

^{2}= 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 y

^{2}= 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

View Answer

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

View Answer

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

View Answer

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.

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