Using a new formulation of the Bezout matrix, we construct bivariate matrix polynomials expressed in a tensor-product Lagrange basis. We use these matrix polynomials to solve common tasks in computer-aided geometric design: for example, we show that these bivariate polynomials can serve as stable and efficient implicit epresentations of plane curves for a variety of curve intersection problems including offset manipulation. This is a joint work with D. Aruliah, R. Corless and A. Shakoori