Answer
${{x}^{2}}+{{\left( y-30.6 \right)}^{2}}=590.49$
Work Step by Step
Equation of circle is ${{\left( x-h \right)}^{2}}+{{\left( y-k \right)}^{2}}={{r}^{2}}$.
Put the center of the circle $\left( 0,30.6 \right)$ and radius $r=24.3$.
$\begin{align}
& {{\left( x-h \right)}^{2}}+{{\left( y-k \right)}^{2}}={{r}^{2}} \\
& {{\left( x-0 \right)}^{2}}+{{\left( y-30.6 \right)}^{2}}={{\left( 24.3 \right)}^{2}} \\
& {{x}^{2}}+{{\left( y-30.6 \right)}^{2}}=590.49 \\
\end{align}$
Thus, the equation of the circle is ${{x}^{2}}+{{\left( y-30.6 \right)}^{2}}=590.49$.
