paraboloid

A paraboloid is a type of curved surface (within three-dimensional space) that is based upon a parabola; specifically, it is circularly-symmetric such that an intersection with any plane through its axis is a parabola. A hyperboloid is the analogous surface based upon a hyperbola. Finite portions of these curved surfaces are used for the mirrors of some types of reflector telescopes: various combinations of such mirrors can reduce the aberrations that occur using spherical mirrors. There is a trade-off because they are generally harder to manufacture than spherical mirrors and they introduce other aberrations. These shapes are examples of quadratic surfaces, as are spheroids and ellipsoids.