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

1. The sections cut by a plane on a right circular cone are called as ______

a) Parabolic sections

b) Conic sections

c) Elliptical sections

d) Hyperbolic sections

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Explanation: The sections cut by a plane on a right circular cone are called as conic sections or conics. The plane cuts the cone on different angles with respect to the axis of the cone to produce different conic sections.

2. Which of the following is a conic section?

a) Circle

b) Rectangle

c) Triangle

d) Square

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Explanation: Circle is a conic section. When the plane cuts the right circular cone at right angles with the axis of the cone, the shape obtained is called as circle. If the angle is oblique we get the other parts of the conic sections.

3. In conics, the _____ is revolving to form two anti-parallel cones joined at the apex.

a) Ellipse

b) Circle

c) Generator

d) Parabola

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Explanation: In conics, the generator is revolving to form two anti-parallel cones joined at the apex. The plane is then made to cut these cones and we get different conic sections. If we cut at right angles with respect to the axis of the cone we get a circle.

4. While cutting, if the plane is at an angle and it cuts all the generators, then the conic formed is called as ______

a) Circle

b) Ellipse

c) Parabola

d) Hyperbola

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Explanation: If the plane cuts all the generators and is at an angle to the axis of the cone, then the resulting conic section is called as ellipse. If the cutting angle was right angle and the plane cuts all the generators then the conic formed would be circle.

5. If the plane cuts at an angle to the axis but does not cut all the generators then what is the name of the conics formed?

a) Ellipse

b) Hyperbola

c) Circle

d) Parabola

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Explanation: If the plane cuts at an angle with respect to the axis and does not cut all the generators then the conics formed is a parabola. If the plane cuts all the generators then the conic section formed is called as ellipse.

6. When the plane cuts the cone at angle parallel to the axis of the cone, then _____ is formed.

a) Hyperbola

b) Parabola

c) Circle

d) Ellipse

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Explanation: When the plane cuts the cone at an angle parallel to the axis of the cone, then the resulting conic section is called as hyperbola. If the plane cuts the cone at an angle with respect to axis of the cone then the resulting conic sections are called as ellipse and parabola.

7. Which of the following is not a conic section?

a) Apex

b) Hyperbola

c) Ellipse

d) Parabola

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Explanation: Conic sections are formed when a plane cuts through the cone at an angle with respect to the axis of the cone. If the angle is right angle then the conics is circle, if the angle is oblique then the resulting conics are parabola and ellipse.

8. The locus of point moving in a plane such that the distance between a fixed point and a fixed straight line is constant is called as ________

a) Conic

b) Rectangle

c) Square

d) Polygon

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Explanation: The locus of a point moving in a plane such that the distance between a fixed point and a fixed straight line is always constant. The fixed straight line is called as directrix and the fixed point is called as focus.

9. The ratio of the distance from the focus to the distance from the directrix is called as eccentricity.

a) True

b) False

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Explanation: The ratio of the distance from the focus to the distance from the directrix is called as eccentricity. It is denoted as e. The value of eccentricity can give information regarding which type of conics it is.

10. Which of the following conics has an eccentricity of unity?

a) Circle

b) Parabola

c) Hyperbola

d) Ellipse

View Answer

Explanation: Eccentricity is defined as the ratio of the distance from the focus to the distance from the directrix. It is denoted as e. The value of eccentricity can give information regarding which type of conics it is. The eccentricity of parabola is unity that is 1.

11. Which of the following has an eccentricity less than one?

a) Circle

b) Parabola

c) Hyperbola

d) Ellipse

View Answer

Explanation: Eccentricity is defined as the ratio of the distance from the focus to the distance from the directrix. It is denoted as e. The value of eccentricity can give information regarding which type of conics it is. The eccentricity of ellipse is less than one.

12. If the distance from the focus is 10 units and the distance from the directrix is 30 units, then what is the eccentricity?

a) 0.3333

b) 0.8333

c) 1.6667

d) 0.0333

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Explanation: Eccentricity is defined as the ratio of the distance from the focus to the distance from the directrix. Hence from the formula of eccentricity, e = 10 ÷ 30 = 0.3333. Since the value of eccentricity is less than one the conic is ellipse.

13. If the value of eccentricity is 12, then what is the name of the conic?

a) Ellipse

b) Hyperbola

c) Parabola

d) Circle

View Answer

Explanation: Eccentricity is defined as the ration of the distance from the focus to the distance from the directrix. It is denoted as e. If the value of eccentricity is greater than unity then the conic section is called as hyperbola.

14. If the distance from the focus is 3 units and the distance from the directrix is 3 units, then how much is the eccentricity?

a) Infinity

b) Zero

c) Unity

d) Less than one

View Answer

Explanation: Eccentricity is defined as the ration of the distance from the focus to the distance from the directrix and it is denoted as e. Hence from the definition, e = 3 ÷ 3 = 1. Hence the value of eccentricity is equal to unity.

15. If the distance from the focus is 2 mm and the distance from the directrix is 0.5 mm then what is the name of the conic section?

a) Circle

b) Ellipse

c) Parabola

d) Hyperbola

View Answer

Explanation: The eccentricity is defined as the ratio of the distance from the focus to the distance from the directrix. It is denoted as e. If the value of the eccentricity is greater than unity then the conic section is called as hyperbola.

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