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Recently, in my calculus two class, we began going over conic sections. After reviewing the definitions of ellipses and hyperbolas - For two given points, the foci, an ellipse is the locus of points such that the sum of/difference between the distance to each focus is constant, respectively - I couldn't help but become curious: does a shape and/or equation for a set of points such that "the product or quotient of the distance to each focus is constant" instead of just the sum or difference? I posed this question to my math instructor too, but he didn't know. (I hope that this is the right section to post this in. It seemed most likely, but I couldn't tell with any certainty which sub-forum to post this on)