Let two lines rotate about the points and so that when the line rotating about has angle with the x axis, the rotating about has angle . Let be the point of intersection, then the angle formed by the lines at is . By the law of sines,
so the equation in polar coordinates is (up to translation and rotation)
The curve is therefore a member of the conchoid of de Sluze family.
In Cartesian coordinates the equation of this curve is
If the origin is moved to (a, 0) then a derivation similar to that given above shows that the equation of the curve in polar coordinates becomes
making it an example of a limacon with a loop.