What is a rectangular hyperbola?

A rectangular hyperbola is a hyperbola containing orthogonal asymptotic lines. Before rectangular hyperbolas were first studied by Menaechmus, general hyperbolas were studied by Euclid and Aristaeus. Apollonius later studied both general and rectangular hyperbolas.

Hyperbolas are centered on a point which is considered the center of the hyperbola. The point on each branch closest to the center is known as the branch's vertex. The vertices are located from a fixed distance from the center. The transverse axis goes through the center from one vertex to the other. Inside each branch are the foci and located at a fixed distance from the center.