Question

A plane intersects both nappes of a double-napped cone but does not go through the vertex of the cone.

What conic section is formed?


hyperbola

parabola

ellipse

circle

Answer 1

It intersects both nappes of the double napped cone, but does not go through the vertex. This weird intersection will create a conic curve that is called the...

Hyperbola!

Answer 2

The cross-section that is obtained on slicing the double napped cone such that it does not pass through the vertex of the cone is:

Hyperbola.

Explanation:

We know when a plane intersects only one nape of a double napped cone then the cross section that is obtained is either a parabola, ellipse or a circle.

But when it passes through both the napes of a double napped cone then the cross-section obtained is a hyperbola.

Hence, the answer is Hyperbola.