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Lemniscate

The lemniscate is the locus of the points for which the product of the distances from the two points (-1, 0) and (1, 0) is constant a2.
Its equation is (x2 + y2)2 - 2 (x2 - y2) + 1 - a4 = 0. The curve will change as the value of parameter "a" changes.