Conic section

The four conical scones in this picture have each had a different slice through them, so they illustrate, the four different kinds of conic section, from left to right, the circle, the ellipse, the parabola and the hyperbola.

A conic section is a curve formed by the intersection of a right circular cone and a plane. There are four types of such curves:

1. A circle, when the plane is parallel to the base of the cone.
2. An ellipse, when the plane makes an angle to the base of the cone.
3. A parabola, when the plane is parallel to the side of the cone.
4. A hyperbola, when the plane cuts both the cone and its extension on the other side of the vertex.

Additionally, there are two degenerate cases:

1. A pair of intersecting straight lines, when the plane cuts the cone and passes through the vertex; these lines may coincide if the lane just touches the cone.
2. A single point, when the plane goes through the vertex without touching the cone elsewhere.