Question

When the plane cuts the nappe (other than the vertex) of the cone, we have the following situations

Column I		Column II
A	When $\beta =90^{\circ }$	1	Section is a parabol
B	When $\alpha <\beta <90^{\circ }$	2	Section is a circle.
C	When $\beta =\alpha$	3	Section is an ellipse.
D	When $0\le \beta <\alpha$	4	Plane cuts through both the nappes and the curve of intersection is a hyperbola.

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= 3,C= 1 ,D= 4
• B. A= 3 ,B=2 ,C=1 ,D=4
• C. A= 2 ,B= 3,C= 4 ,D=1
• D. A= 2 ,B=1 ,C=3 ,D=4

Answer 1

Answer: (A)

A. When $\beta =90^{\circ }$; the section is a circle.
B. When $\alpha <\beta <90^{\circ }$; the section is an ellipse.
C. When $\beta =\alpha$; the section is a parabola.
D. When $0\le \beta <\alpha$; the plane cuts through both the nappes and the curves of intersection is hyperbola.
(in each of $A,B$ and $C$, the plane cuts entirely across one nappe of the cone).