Answer
${{\left( x+4 \right)}^{2}}+{{\left( y-9 \right)}^{2}}=20$
Work Step by Step
The center of the circle is $\left( h,k \right)=\left( -4,9 \right)$, and the radius is $r=2\sqrt{5}$.
Now, put the value of the center $\left( h,k \right)=\left( -4,9 \right)$ and radius $r=2\sqrt{5}$ in the formula,
${{\left( x-h \right)}^{2}}+{{\left( y-k \right)}^{2}}={{r}^{2}}$
Now, it is written as,
$\begin{align}
& {{\left( x-\left( -4 \right) \right)}^{2}}+{{\left( y-9 \right)}^{2}}={{\left( 2\sqrt{5} \right)}^{2}} \\
& {{\left( x+4 \right)}^{2}}+{{\left( y-9 \right)}^{2}}=20
\end{align}$
Thus, the equation of the circle is ${{\left( x+4 \right)}^{2}}+{{\left( y-9 \right)}^{2}}=20$.
