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
• B. P - 1, Q - 2, S - 3, R - 4
• C. P - 1, Q - 2, S - 3, R - 4
• D. P - 2, Q - 1, R - 3, S - 4

Answer 1

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.