\(\bf \textit{equation of a circle}\\\\
(x-{{ h}})^2+(y-{{ k}})^2={{ r}}^2
\qquad
\begin{cases}
center\ ({{ h}},{{ k}})\\
radius={{ r}}\\
----------\\
center\ (0,1)\to
\begin{cases}
h=0\\
k=1
\end{cases}\\
r=3
\end{cases}
\\\\\\
(x-0)^2+(y-1)^2=3^2\implies x^2+(y-1)^2=9
\\\\\\
(y-1)^2=9-x^2\implies y=\sqrt{9-x^2}+1\\\\
-----------------------------\\\\
\textit{where do the parabola and circle intersect? set them to equal}
\\\\\\\)
\(\bf \begin{cases}
y=x^2\\\\
y=\sqrt{9-x^2}+1
\end{cases}\qquad y=y\implies x^2=\sqrt{9-x^2}+1\)
solve for "x"
