6 May
2013
6 May
'13
4:02 a.m.
On the plane, assume the foci are at (-1,0) and (1,0): The ellipse is the locus of points whose sum of distances to the foci is a constant. The ovals of Cassini is the locus of points whose product of distances to the foci is a constant. (See < http://en.wikipedia.org/wiki/File:Line_of_Cassini.svg >.) Can you guess the evolution of the locus of points whose exponentiation of their distances to the foci is a constant, as that constant increases from 0 to, say, 2 ??? (I certainly didn't!) --Dan