A quadric whose equation in a suitable coordinate system isThe yz-plane and the zx-plane are planes of symmetry. Sections by planes parallel to the xy-plane are hyperbolas, the section by the xy-plane itself being a pair of straight lines. Sections by planes parallel to the other axial planes are parabolas. Planes through the z-axis cut the paraboloid in parabolas with vertex at the origin. The origin is a saddle-point.