For a Hyperbola with with Inversion Center at the center, the Inverse Curve

(1) | |||

(2) |

is a Lemniscate.

For an Inversion Center at the Vertex, the Inverse Curve

(3) | |||

(4) |

is a Right Strophoid.

For an Inversion Center at the Focus, the Inverse Curve

(5) | |||

(6) |

is a Limaçon, where is the Eccentricity.

For a Hyperbola with and Inversion Center at the
Vertex, the Inverse Curve

(7) | |||

(8) |

is a Maclaurin Trisectrix.

**References**

Lawrence, J. D. *A Catalog of Special Plane Curves.* New York: Dover, p. 203, 1972.

© 1996-9

1999-05-25