Analytic types of plane curve singularities defined by weighted homogeneous polynomials

We classify analytically isolated plane curve singularities defined by weighted homogeneous polynomials f(y, z), which are not topologically equivalent to homogeneous polynomials, in an elementary way. Moreover, in preparation for the proof of the above analytic classification theorem, assuming that g(y, z) either satisfies the same property as the above f does or is homogeneous, then we prove easily that the weights of the above g determine the topological type of g and conversely. So, this gives another easy proof for the topological classification theorem of quasihomogenous singularities in C-2, which was already known. Also, as an application, it can be shown that for a given h, where h(w(1),..., w(n)) is a quasihomogeneous holomorphic function with an isolated singularity at the origin or h(w(1)) = w(1)(p) with a positive integer p, analytic types of isolated hypersurface singularities defined by f + h are easily classified where f is defined just as above.