The elliptic hyperboloid is the generalization of the Hyperboloid to three distinct semimajor axes. The
elliptic hyperboloid of one sheet is a Ruled Surface and has Cartesian equation

(1) |

(2) | |||

(3) | |||

(4) |

for , or

(5) | |||

(6) | |||

(7) |

or

(8) | |||

(9) | |||

(10) |

The two-sheeted elliptic hyperboloid oriented along the *z*-Axis has Cartesian equation

(11) |

(12) | |||

(13) | |||

(14) |

The two-sheeted elliptic hyperboloid oriented along the

(15) |

(16) | |||

(17) | |||

(18) |

**References**

Gray, A. *Modern Differential Geometry of Curves and Surfaces.*
Boca Raton, FL: CRC Press, pp. 296-297, 1993.

© 1996-9

1999-05-25