A quadric whose equation in a suitable coordinate system is

The 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.

Hyperbolic paraboloid in normal form