hyperboloid of two sheets

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A quadric whose equation in a suitable coordinate system isThe axial planes are planes of symmetry. The section by a plane z=k parallel to the xy-plane, is, when non-empty, an ellipse (a circle if a=b). When k lies between −c and c, the plane z=k has no points of intersection with the hyperboloid, and the hyperboloid is thus in two pieces or sheets. Sections by planes parallel to the other two axial planes are hyperbolas. Planes through the z-axis cut the hyperboloid in hyperbolas with vertices at (0, 0, c) and (0, 0,−c).

Subjects: Mathematics.

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