|a geometric surface consisting of one sheet, or of two sheets separated by a finite distance, whose sections parallel to the three coordinate planes are hyperbolas or ellipses. Equations x²/a² + y²/b² -- z²/c² = 1 (one sheet) or x²/a² -- y²/b² -- z²/c² = 1 (two sheets) where a, b, and c are constants|
|hyperboloid (hī-pûr'bə-loid') Pronunciation Key
Either of two surfaces generated by rotating a hyperbola about either of its main axes and having a finite center, with certain plane sections that are hyperbolas and others that are ellipses or circles.
the open surface generated by revolving a hyperbola (q.v.) about either of its axes. If the tranverse axis of the surface lies along the x axis and its centre lies at the origin and if a, b, and c are the principal semi-axes, then the general equation of the surface is expressed as x2/a2 y2/b2 - z2/c2 = 1.
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