Conchoid of de Sluze

The conchoid of de Sluze is the cubic curve first constructed by René de Sluze in 1662. It is given by the implicit equation

(1)

or the polar equation

(2)

This can be written in parametric form as

			(3)
			(4)

The conchoid of de Sluze has a singular point at the origin which is a crunode for , a cusp for , and an acnode for .

It has curvature and tangential angle

			(5)
			(6)

The curve has a loop if , in which case the loop is swept out by . The area of the loop is

(7)