Plane Curves with Pseudo-Rhamphoid Cusps

A necessary condition that the parametric equations

x = f(T), y = g(T)                            (1)

represent the plane algebraic curve U(x, y) = 0 is that U [f(T), g(T)] = 0 in the parameter T. This condition merely states that the points given by the equations (1) are points of the curve U(x, y) = 0, and does not imply that to every point of the curve there corresponds a value of T.