Plane curve

Summary

A plane algebraic curve is a curve in the affine or projective plane defined by one polynomial equation. Its degree is the degree of that polynomial. By Bézout's theorem, it is the number of points in which a general line meets the curve. Lines, conics and cubics are the plane curves of degree $1$, $2$ and $3$. More generally, in geometry a plane curve is any curve that lies in a plane.