A quadric whose equation in a suitable coordinate system is
Here the yz‐plane and the zx‐plane are planes of symmetry. Sections by planes z = k, where k ≥ 0, are ellipses. Sections by planes parallel to the yz‐plane and to the zx‐plane are parabolas. Planes through the z‐axis cut the paraboloid in parabolas with vertex at the origin.