Conic sections are formed on a plane when that plane slices through the edge of one or both of a pair of right circular cones stacked tip to tip. Whether the result is a circle, ellipse, parabola, or hyperbola depends only upon the angle at which the plane slices through. Conic sections are described mathematically by quadratic equations—some of which contain more than one variable.
When the edge of a single or stacked pair of right circular cones is sliced by a plane, the curved cross section formed by the plane and cone is called a conic section. The four main conic sections are the circle, the parabola, the ellipse, and the hyperbola (see Figure 1).
Figure 1. Creating conic sections.