[hī′pər·bə‚lȯid əv ′wən ‚shēt] (mathematics) A surface whose equation in stardard form is (x2/ a2) + (y2/ b2) - (z2/ c2) = 1, so that it is in one piece, and cuts planes perpendicular to the x or y axes in hyperbolas and planes perpendicular to the z axis in ellipses.