Cubic plane curve

A cubic plane curve is a type of algebraic curve defined by a polynomial equation of degree three in two variables, typically represented in the form: \[ F(x, y) = ax^3 + bx^2y + cxy^2 + dy^3 + ex^2 + fy^2 + gx + hy + i = 0 \] where \(a, b, c, d, e, f, g, h, i\) are constants, and the