Conic Section

A conic section is a curve obtained by intersecting a cone (more precisely, a circular conical surface) with a plane. The three type of conics are the hyperbola, ellipse, and parabola. (The circle is a special case of the ellipse, and there are degenerate cases like a pair of intersecting lines, a point, a double line, etc.) In polar coordinates, a conic section with one focus at the origin and the other focus (if any) on the axis, is given by the equation

,

where is the eccentricity and is the semilatus rectum. As above, for , we have a circle, for , we obtain a ellipse, for a parabola, and for a hyperbola.

Conic sections are important in astronomy: the orbits of two massive objects that interact according to Newton's law of universal gravitation are conic sections if their common center of mass is considered to be at rest.