Trident curve

In mathematics, a trident curve (also trident of Newton or parabola of Descartes) is any member of the family of curves that have the formula:
Trident curves are cubic plane curves with an ordinary double point in the real projective plane at "x" = 0, "y" = 1, "z" = 0; if we substitute "x" =  and "y" =  into the equation of the trident curve, we get
which has an ordinary double point at the origin. Trident curves are therefore rational plane algebraic curves of genus zero.