PARABOLOID, HYPERBOLOID.) The equations of the conoids are: f or the sphere; z2 = 1 for the prolate spheroid; = I, oblate b2 b2 2 spheroid; = 4 px, for the paraboloid; a2 — b2 = for the hyperboloid of one sheet ; x -y2 2 Z2 = for the hyperboloid a2 b2 two sheets. These "surfaces of rotation," or "revolutes," areonly special cases of ellipsoid, paraboloid, hyperboloid (q.v.) as named in analytic geometry.