Cubic plane curve

In mathematics, a cubic plane curve is a plane algebraic curve C defined by a cubic equation F(x, y, z) = 0 applied to homogeneous coordinates x:y:z for the projective plane; or the inhomogeneous version for the affine space determined by setting z = 1 in such an equation. Here F is a non-zero linear combination of the third-degree monomials x3, y3, z3, x2y, x2z, y2x, y2z, z2x, z2y, xyz.

Cubic plane curve

In mathematics, a cubic plane curve is a plane algebraic curve C defined by a cubic equation F(x, y, z) = 0 applied to homogeneous coordinates x:y:z for the projective plane; or the inhomogeneous version for the affine space determined by setting z = 1 in such an equation. Here F is a non-zero linear combination of the third-degree monomials x3, y3, z3, x2y, x2z, y2x, y2z, z2x, z2y, xyz.