The number of distinct points common to the graphs of $x^2+y^2=9$ and $y^2=9$ is:
$\textbf{(A) }\text{infinitely many}\qquad \textbf{(B) }\text{four}\qquad \textbf{(C) }\text{two}\qquad \textbf{(D) }\text{one}\qquad \textbf{(E) }\text{none}$
Solve the second equation by taking the square root of both sides.
\[y^2=9\]
\[y=\pm3\]
Solve the first equation by substituting $y^2$ into the first equation then solving for $x$.
\[x^2+9=9\]
\[x^2=0\]
\[x=0\]
The two solutions are $(0,3)$ and $(0,-3)$, so the answer is $\boxed{\textbf{(C)}}$.