This set of Advanced Engineering Drawing Interview Questions & Answers focuses on “Basics of Conic Sections – 3”.

1. Choose the correct option.

View Answer

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. Match the following.

1. E < 1 i. Rectangular hyperbola

2. E = 1 ii. Hyperbola

3. E > 1 iii. Ellipse

4. E > 1 iv. Parabola

a) 1, i; 2, ii; 3, iii; 4, iv

b) 1, ii; 2, iii; 3, iv; 4, i

c) 1, iii; 2, iv; 3, ii; 4, i

d) 1, iv; 2, iii; 3, ii; 4, i

View Answer

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 middle. The cross-section is __________

a) Circle

b) Parabola

c) Hyperbola

d) Ellipse

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Explanation: A cone is formed by reducing the cross-section of circle the point. So there exist circles along the cone parallel to base. Since the given plane is parallel to base of the regular cone. The cross-section 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

View Answer

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

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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

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Explanation: If the cutting plane makes angle less than exterior angle of the cone the cross-section 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

View Answer

Explanation: Given is a plane which is inclined but cutting all the generators so it will be 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 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

View Answer

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

View Answer

Explanation: The eccentricity is the ratio of distance from a point on 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

View Answer

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 rectangular hyperbola.

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