A parabola is an open curve in the plane, defined as the set of all points whose distances from a fixed point, called the focus, and a fixed line, called the directrix, are equal.
Algebraically, a parabola in the Cartesian plane with vertical axis is a function defined by an equation of the form
\[(x-h)^2 = 4p(y-k)\]
where the point \((h,k)\) is the vertex of the parabola.
Figure 1: A parabola in the Cartesian plane.
A parabola has important reflection properties. See the article on conics for an exposition.
- [MLA] “parabola.” Platonic Realms Interactive Mathematics Encyclopedia. Platonic Realms, 27 Mar 2013. Web. 27 Mar 2013. <http://platonicrealms.com/>
- [APA] parabola (27 Mar 2013). Retrieved 27 Mar 2013 from the Platonic Realms Interactive Mathematics Encyclopedia: http://platonicrealms.com/encyclopedia/parabola/
See also: ellipse, hyperbola, quadratic