Cartesian trident

The plane curve given by the equation a x y | = | (a + x)(a - x)(2a - x) | = | x^3 - 2a x^2 - a^2 x + 2a^3, which, solving for y, gives y = ((a + x)(a - x)(2a - x))/(a x). The plots above are for a = 0.5 to 3.

trident | trident of Newton

René Descartes