Abstract: In this paper, an optimal method of implicitization for planar rational curves is presented. The coefficients of the implicit equation is proved to be the minimum solving vector of a real quadratic form in fact, or a nontrivial solution of a homogeneous linear equations. Because of the implicit equation’s complexity and the numerical computation in practice, an approximate implicitization optimal method using lower degree implicit equations for rational curves is proposed also, and the resultant implicit curve is interpolatory and GC 1. Finally, numerical examples show the method’s efficiency.