Question

The double cone is intersected by a vertical plane passing through the point where the tips of the cones meet. What is the shape of the cross section formed?

Answer 1

Answer:

The cross-section that is obtained by this slicing is:

Hyperbola.

Step-by-step explanation:

If a double cone is intersected by a vertical plane passing through the point where the tips of the cones meet then the shape of the cross-section that is obtained by this slicing will be a hyperbola.

( Since the plane cuts both the sections of the cone and hence we will get a curve on both the cones opening in the opposite direction and hence such a figure that is obtained is called a hyperbola)

Answer 2

Answer:

A pair of intersecting lines .

Step-by-step explanation:

An  hyperbola is formed when a vertical plane intersect the two cones, but doesn't pass through the point where the tips of the cones meet. Vertical planes that pass through the vertex of the cones will intersect the cone in a pair of intersecting lines. This is a case of degenerate conics and some authors do not consider them to be conics at all.

In the figure attached, an hyperbola is shown. In this case, a = 0 and the asymptotes are the pair of intersecting lines.