Why are two definitions of ellipses equivalent?
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In classical geometry an ellipse is usually defined as the locus of points in the plane such that the distances from each point to the two foci have a given sum. When we speak of an ellipse analytically, we usually describe it as a circle that has been squashed in one direction, i.e. something similar to the curve $x^2+(y/b)^2 = 1$. "Everyone knows" that these two definitions yield the same family of shapes. But how can that be proved?
geometry analytic-geometry conic-sections
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asked Oct 29 '13 at 10:28
Henning Makholm
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