Serpentine curve

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A serpentine curve is a curve whose equation is of the form x2y + aby − a2x = 0, where ab > 0. Equivalently, it has a parametric representation x = acot(t),y = bsin(t)cos(t). Serpentine curves were studied by L'Hopital and Huygens, and named and classified by Newton.

The serpentine curve for a = b = 1.
The serpentine curve for a = b = 1.

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