Serpentine curve

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

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

External links

• MathWorld - Serpentine Equation
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