Cassinian　Ovals

Cassinian oval is a generalization of the lemniscate of Bernoulli.

The definition of Cassinian ovals is as follows.

Def：The locus S(a,b) of points for which the product of the distances from two fixed points F,F' is a constant b²,where distannce(F,F')=2a

Thus

　　　　S(a,b)={ P | PF*PF' = b² }

Implicot Form is as follows.

　　　　cassini( a, b )(x, y) = (x²+y²+a²)²-b⁴-4a²x²

Note that cassini ( b, b) is a lemniacate of Bernoulli and cassini( 0,b) is a circle.

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