Let be a curve, let be a fixed point (the pole), and
let be a second fixed point. Let and be points on a line through meeting at
such that .
The locus of and
is called the strophoid of
with respect to the pole and fixed point . Let be represented parametrically by , and let and . Then the equation of the strophoid is

(1)

(2)

where

(3)

The name strophoid means "belt with a twist," and was proposed by Montucci in 1846 (MacTutor Archive). The polar form for a general strophoid is

(4)

If , the curve is a right
strophoid. The following table gives the strophoids of some common curves.