# hyperbola

A hyperbola is an open curve in the plane with two distinct branches, defined as the set of all points the difference of whose distances from two fixed points is a constant.

Algebraically, a hyperbola in the Cartesian plane with horizontal axis is a relation defined by an equation of the form

\[\displaystyle\frac{(x-h)^2}{a^2}-\frac{(y-k)^2}{b^2}=r^2\]

where the point \((h,k)\) is the center of the hyperbola. The major axis of the hyperbola is vertical if the \(y\) term is positive and the \(x\) term is negative.

A hyperbola also has directices and important reflection properties. See the article on conics for an exposition.