We classify analytically isolated plane curve singularities defined by weighted homogeneous polynomials
f
(
y
,
z
)
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
)
g(y,z)
either satisfies the same property as the above
f
f
does or is homogeneous, then we prove easily that the weights of the above
g
g
determine the topological type of
g
g
and conversely. So, this gives another easy proof for the topological classification theorem of quasihomogenous singularities in
C
2
\mathbb {C}^{2}
, which was already known. Also, as an application, it can be shown that for a given
h
h
, where
h
(
w
1
,
…
,
w
n
)
h(w_{1},\dots ,w_{n})
is a quasihomogeneous holomorphic function with an isolated singularity at the origin or
h
(
w
1
)
=
w
1
p
h(w_{1})=w^{p}_{1}
with a positive integer
p
p
, analytic types of isolated hypersurface singularities defined by
f
+
h
f+h
are easily classified where
f
f
is defined just as above.