Trident curve

In mathematics, a trident curve is any member of the family of curves that have the formula:
Image:Newton_trident.svg|thumb|300px|trident curve with a = b = c = d = 1
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
Image:Newton trident y=inf.svg|thumb|300px|Trident curve at y = ∞ with a = b = c = d = 1. This curve in some part resembles Folium of Descartes
which has an ordinary double point at the origin. Trident curves are therefore rational plane algebraic curves of genus zero.
Solving for y, we get
Solving for x, we get