Let a Cone of opening parameter and vertex at intersect a Sphere of
Radius centered at
, with the Cone oriented such that its axis does not pass through the
center of the Sphere. Then the equations of the curve of intersection are

(1) | |||

(2) |

Combining (1) and (2) gives

(3) |

(4) |

If the Cone-Sphere intersection is *on-axis* so that a Cone of opening parameter and vertex at
is oriented with its Axis along a radial of the Sphere of radius centered at , then
the equations of the curve of intersection are

(5) | |||

(6) |

Combining (5) and (6) gives

(7) |

(8) |

(9) |

(10) |

So the curve of intersection is planar. Plugging (10) into (5) shows that the curve is actually a Circle, with Radius given by

(11) |

© 1996-9

1999-05-26