Serpentine curve

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A serpentine curve is a curve whose equation is of the form x^2y+a^2y-abx=0, where ab > 0. Equivalently, it has a parametric representation x=a\cot(t), y=b\sin (t)\cos(t), or functional representation y=\frac{abx}{x^2+a^2}. Serpentine curves were studied by L'Hôpital and Huygens, and named and classified by Newton.

The serpentine curve for a=b=1.

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