Cassini Ovals and Other Curves

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Fix two points and
in the plane and consider the locus of a point
so that the sum of the distances from
to
and
equals some constant. For different arithmetic operations (sum, difference, quotient, or product), this set takes on different shapes.
Contributed by: Chris Boucher (March 2011)
Open content licensed under CC BY-NC-SA
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"Cassini Ovals and Other Curves"
http://demonstrations.wolfram.com/CassiniOvalsAndOtherCurves/
Wolfram Demonstrations Project
Published: March 7 2011