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An ellipse is the set of all points X in 2d space such that the the sum of the distances AX and BX is a given constant constant, where A and B are given points. What is the name for the set of all points X in 3d space such that the sum of the distances AX and BX is a given constant, where A and B are given points?

user107952
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1 Answers1

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If you rotate your elipse defined by $A$, $B$ and that distance around the axis $AB$, you obtain a prolate spheroid, which is a special kind of ellipsoid.

MvG
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