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.