In mathematics, a paraboloid is a quadric, a type of surface in three dimensions, described by the equation:

(elliptic paraboloid),


(hyperbolic paraboloid).

With a=b an elliptic paraboloid is a paraboloid of revolution: a surface obtained by revolving a parabola around its axis. It the shape used by the parabolic reflectors used in mirrors, antenna dishes, and the like.

A point light source at the focal point produces a parallel light beam. This also works the other way around: a parallel beam of light incident on the paraboloid is concentrated at the focal point. This applies also for other waves, hence parabolic antennas.