A

conic section is a curve that follows the intersection between a and a .

When a intersects with a , the intersection between the surface and the solid can take four different shapes — a circle, an , a , or a . If the plane does not intersect the base of the cone the conic section is an ellipse.

Notice that the is a special case of the ellipse when the plane is parallel to the base of the cone.
If the plane is parallel to one side of the cone the conic section is a parabola.

In the remaining cases the plane will be able to intersect a second cone, which is the reflection about the vertex of the original cone. The resulting conic section will be a hyperbola.