Cubic plane curve
（重定向自Cubic curve）
![A selection of cubic curves. Click the image to see information page for details.](/Images/godic/202501/07/CubicCurve.svg4837.png")
![Singular cubic y2 = x2 · (x + 1). A parametrization is given by t → (t2 − 1, t · (t2 − 1))](/Images/godic/202501/07/Cubic_with_double_point.svg4837.png")
![Example of Thomson cubic (black curve). X is on the cubic, such that the isogonal conjugate of X (X') is on the line X(2)-X.](/Images/godic/202501/07/Thomson_cubic.svg4837.png")
In mathematics, a cubic plane curve is a plane algebraic curve C defined by a cubic equation
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