Question

if a right circular cone is intersected by a plane that passes through only one nappe of the cone but is not parallel to an edge of the cone, as the picture below, what shape is produced?

Answer 1

An ellipse

Explanation:

A p e x

Answer 2

C. An ellipse

Explanation:

If you cut a cone on the side with an angle that will produce an ellipse-shaped plane.

if you were to cut the cone perpendicularly to its height (as if the double cone on the picture was straight up), you would get a circle as the plane, because it would be a transversal cut of a circular cone.

If you cut it with an angle, you're stretching the circle... so you'll have an ellipse.

It is NOT a parabola NOR a hyperbola, since both would require the cross-section to go through the base... which it does not in this problem. Please refer to the image below.