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Question

# Match the following. In column 1, we are given a two dimensional projection of a right circular cone and a plane with dotted line. Match them with resulting conic given in column 2.

A

P - 2, Q - 1, S - 4, R - 3

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B

P - 1, Q - 2, S - 3, R - 4

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C

P - 1, Q - 2, S - 3, R - 4

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D

P - 2, Q - 1, R - 3, S - 4

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Solution

## The correct option is D P - 2, Q - 1, R - 3, S - 4 Circle, Parabola, Ellipse and Hyperbola are the conics we are given in column 2. We get all of them by taking a section of a right circular cone by a plane. Depending on the orientation of the plane, we get different types of conics. Circle If we cut the cone with a plane parallel to the base, we get a circle parabola By a plane parallel to the generator (see figure) Ellipse By a plane not parallel to any generator nor parallel or perpendicular the base Hyperbola The condition of the plane is same as that of ellipse.

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