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


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.

Figure 1: A hyperbola in the Cartesian plane.

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

Citation Info

  • [MLA] “hyperbola.” Platonic Realms Interactive Mathematics Encyclopedia. Platonic Realms, 27 Mar 2013. Web. 27 Mar 2013. <>
  • [APA] hyperbola (27 Mar 2013). Retrieved 27 Mar 2013 from the Platonic Realms Interactive Mathematics Encyclopedia:


Get the ultimate math study-guide Math & Me: Embracing Successproduct thumbnail image Available in the Math Store
detail from Escher pic Belvedere

Are you a mathematical artist?

Platonic Realms is preparing an online gallery space to showcase and market the works of painters, sculptors, and other artists working in a tangible medium.

If your work celebrates mathematical themes we want to hear from you!

Please let us know about yourself using the contact page.