Conic Sections Model

Slice a cone with a flat plane, and the shape of the cut depends on the angle of the slice. A cut perpendicular to the cone’s axis gives a circle; a tilted cut through one side gives an ellipse; a steeper cut parallel to the cone’s side gives a parabola; and a cut through both halves of a double cone gives a hyperbola.

These four curves appear throughout mathematics, physics, astronomy and engineering — from planetary orbits to satellite dishes and telescope mirrors.