Question

When the plane cuts at the vertex of the cone, then we have the following situations.

Column I		Column II
A	When $\alpha <\beta \le 90^{\circ }$	1	Section is a pair of intersecting straight lines. (degenerate case of hyperbola)
B	When $\beta =\alpha$	2	Section is a point.
C	When $0\le \beta <\alpha$	3	Plane contains a generator of the cone and the section is a straight line. (degenerate case of parabola)

Here, $\beta$ is the angle made by the intersecting plane with the vertical axis of cone and $\alpha$ is the angle between the generator and vertical axis of cone. Then, match the terms of Column I with terms of Column II and choose the correct option from the codes given below.

• A. A= 2 ,B= 1 ,C= 3
• B. A= 1 ,B= 3 ,C= 2
• C. A=2 ,B= 3 ,C= 1
• D. A=3 ,B= 2 ,C= 1

Answer 1

Answer: (C)

A. When $\alpha <\beta \le 90^{\circ }$, then section is a point.
B. When $\beta =\alpha$, the plane contains a generator of the cone and the section is a straight line.
It is the degenerate case of parabola.
C. When $0\le \beta <\alpha$, the section is a pair of intersecting straight lines. It is the degenerate case of a hyperbola.