Lemniscate of Booth

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In algebraic geometry, the lemniscate of Booth, also called the Hippopede of Proclus, is a plane algebraic curve of degree four and genus zero, with equation

It has an ordinary double point at the origin, and two others on the line at infinity in the complex projective plane. When c > 1, it consists of a single real oval, and when 0 < c < 1 it forms a lemniscate, or figure-eight, figure. When c = 1 it reduces to two tangent circles, and when c < 0 it has no real points.

The special case c = 0.5 produces the familiar lemniscate of Bernoulli.