This set of Engineering Drawing Multiple Choice Questions & Answers (MCQs) focuses on “Construction of Parabola – 2”.

1. Which of the following designs do not require the parabolic curve?

a) Light reflectors

b) Sound reflectors

c) Cooling towers

d) Arches

View Answer

Explanation: The engineering curves play a major role in designing. We use parabolic curves in designing arches, bridges, light reflectors, sound reflectors. Cooling towers need hyperbolic curves.

2. Which of the following design requires the parabolic curves?

a) Cooling towers

b) Water channels

c) Stuffing box

d) Light reflectors

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Explanation: The engineering curves play a major role in designing. We use parabolic curves in designing arches, bridges, light reflectors, sound reflectors. Cooling towers and water channels need hyperbolic curves. Whereas stuffing box design needs the elliptical curve.

3. Which of the following equations belongs to the parabolic curve?

a) Y^{2}+X^{2} = -1

b) Y = X

c) Y = 3(X^{2}-1)

d) XY = 1

View Answer

Explanation: The standard form of the parabolic curve is (X-h)

^{2}= 4p(Y-k), where the focus is (h, k+p) and Y=k-p is the directrix. Hence the given equation, Y=3(X

^{2}-1), which can be modified as 4*(1/12)*(Y-(-3))=(X-0)

^{2}when plotted gives a parabola, as it is similar to the standard equation.

4. The focus point of the parabolic equation Y = 3(X^{2}-1) is ______

a) (1, 3)

b) (⅓, 1)

c) (0, 1/12-3)

d) (1/12+3, 0)

View Answer

Explanation: The standard form of parabolic curve is (X-h)

^{2}= 4p(Y-k), where the focus is (h, k+p) and Y=k-p is the directrix. The given equation, Y=3(X

^{2}-1), which can be modified as 4*(1/12)*(Y-(-3))=(X-0)

^{2}, where h=0, p = 1/12, and k=-3. Hence the focus is (0, 1/12-3).

5. The directrix of the parabolic equation Y = 3(X^{2}-1) is ______

a) Y = -37/12

b) Y = 3

c) Y = 1

d) Y = -3/14

View Answer

Explanation: The standard form of parabolic curve is (X-h)

^{2}= 4p(Y-k), where the focus is (h, k+p) and Y=k-p is the directrix. The given equation, Y=3(X

^{2}-1), which can be modified as 4*(1/12)*(Y-(-3))=(X-0)

^{2}, where h=0, p = 1/12, and k=-3. Hence the line of directrix is Y = -3-1/12 = -37/12.

6. Which of the following possibly be the eccentricity of the parabola?

a) 1

b) ½

c) 3/2

d) 4

View Answer

Explanation: Eccentricity is the ratio of the distance from the focus to the pint on the curve to the perpendicular distance from the directrix to the point on the curve, for parabola both the distances are equal. So the eccentricity of the parabola is one.

7. The standard form of parabolic curve is (X-h)^{2} = 4p(Y-k).

a) True

b) False

View Answer

Explanation: The standard form of the parabolic curve is (X-h)

^{2}= 4p(Y-k), where the focus is (h, k+p) and Y=k-p is the directrix, it is because the parabola is the locus of points P which is equidistant from a fixed point called focus and the fixed-line directrix.

8. Which of the following method is used for construction parabolic curves?

a) Rectangular method

b) Arc of the circle method

c) Concentric circle method

d) Oblong method

View Answer

Explanation: Rectangle method is used for the construction of parabola. For the construction of ellipse, we use Arc of circle method, concentric circle method, oblong method, a loop of the thread method, trammel method.

9. Which of the following is used for the construction of ellipse?

a) Rectangular method

b) Parallelogram method

c) Concentric circle method

d) Tangent method

View Answer

Explanation: For the construction of ellipse we use the concentric method, trammel method. Rectangle method, parallelogram method, and tangent methods are used for the construction of parabola.

10. The length of the latus rectum is four times the focal length for the parabolic curve.

a) True

b) False

View Answer

Explanation: The latus rectum is the line perpendicular to the major axis, passing through the focus, and has its endpoints on the curve. For parabola, the length of the latus rectum is four times the focal length.

11. The opening of the parabola for the equation Y^{2} = 4ax, is on _______

a) The negative side of X-axis

b) The positive side of X-axis

c) The negative side of Y-axis

d) The positive side of Y-axis

View Answer

Explanation: For the parabolic curve of equation Y

^{2}= 4ax, has the focus at (a,0) and the directrix is X=-a, hence the opening of the curve will be towards the Positive side of X-axis and X-axis is also considered as the axis of symmetry.

12. The opening of the parabola for the equation Y^{2} = -4ax, is on the _______

a) The negative side of X-axis

b) The positive side of X-axis

c) The negative side of Y-axis

d) The positive side of Y-axis

View Answer

Explanation: For the parabolic curve of equation Y

^{2}= -4ax, has the focus at (-a,0) and the directrix is X=a, hence the opening of the curve will be towards the Negative side of X-axis and X-axis is also considered as the axis of symmetry.

13. The opening of the parabola for the equation X^{2} = 4aY, is on the _______

a) The negative side of X-axis

b) The positive side of X-axis

c) The negative side of Y-axis

d) The positive side of Y-axis

View Answer

Explanation: For the parabolic curve of equation X

^{2}= 4aY, has the focus at (0, a) and the directrix is Y=-a, hence the opening of the curve will be towards the Positive side of Y-axis and Y-axis is also considered as the axis of symmetry.

14. The opening of the parabola for the equation X^{2} = -4aY, is on the _______

a) The negative side of X-axis

b) The positive side of X-axis

c) The negative side of Y-axis

d) The positive side of Y-axis

View Answer

Explanation: For the parabolic curve of equation X

^{2}= -4aY, has the focus at (0,-a) and the directrix is Y=a, hence the opening of the curve will be towards the negative side of Y-axis and Y-axis is also considered as the axis of symmetry.

15. The equation of the directrix line is X=-a, and the focus point is at (a,0), then where is the vertex of the parabola?

a) (0, 0)

b) (a/2, 0)

c) (-a/2, 0)

d) (0, a/2)

View Answer

Explanation: Vertex of the parabola is the midpoint of the perpendicular line from the focus to the directrix. Here the focus is (a, 0) and directrix is X=-a, hence the perpendicular line from focus cuts the directrix at (-a, 0). Hence the vertex is the midpoint (0, 0).

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