  Let X be a set of smooth points in P^2, and I = \oplus_{t >= d} I_t the
defining ideal of X. In this paper, we give a set of defining equations for the
Rees algebra R(I_{d+1}) of the ideal generated by I_{d+1}. This study give
information to completely answer questions on the defining ideals of projective
embeddings of the blowup of P^2 along the points in X, which has been studied
by many authors. In this paper, we also study the asymptotic behaviour of the
Rees algebras R(I_t) of the ideal generated by I_t, as t gets large.
