Serpentine curve explained

A serpentine curve is a curve whose equation is of the form

x^2y+a^2y-abx=0, ab>0.

Equivalently, it has a parametric representation

x=a\cot(t)

y=b\sin(t)\cos(t),

or functional representation

y=	abx
	x^2+a²

The curve has an inflection point at the origin. It has local extrema at

x=\pma

, with a maximum value of

y=b/2

and a minimum value of

y=-b/2

History

Serpentine curves were studied by L'Hôpital and Huygens, and named and classified by Newton.