Note: Do not rely on this information. It is very old.
Quadric Surface is one which can be cut by any straight line in two points. It is, therefore, a surface of the second order, and any plane section of it is a conic, those sections given by parallel planes being similar to each other. The following are examples of quadric surfaces: - (1) Ellipsoids including prolate and oblate spheroids, with the sphere as a special case.
(2) Hyperboloids of one sheet and of two sheets with the cone as a special case.
(3) Cylinder on elliptic, circular or hyperbolic base, which may reduce to a pair of intersecting planes.
(4) Elliptic and hyperbolic paraboloids.
(5) A cylinder on parabolic base.
(6) A pair of parallel planes.