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# parabola

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.

Citation Info

• [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/