Conchoid of de Sluze

In algebraic geometry, the conchoids of de Sluze are a family of plane curves studied in 1662 by Walloon mathematician René François Walter, baron de Sluze.

[1][2] The curves are defined by the polar equation In cartesian coordinates, the curves satisfy the implicit equation except that for a = 0 the implicit form has an acnode (0,0) not present in polar form.

They are rational, circular, cubic plane curves.

The point most distant from the asymptote is (1 + a, 0).

The area of the loop is Four of the family have names of their own: