Answer
${{\left( x+4 \right)}^{2}}+{{\left( y-3 \right)}^{2}}=18$
Work Step by Step
Standard equation of the circle is:
${{\left( x-h \right)}^{2}}+{{\left( y-k \right)}^{2}}={{r}^{2}}$
Where, the center coordinates are $\left( h,k \right)$ and $\left( x,y \right)$ is any point on the circumference and $r$ is the radius of the circle.
$\begin{align}
& {{\left( x-h \right)}^{2}}+{{\left( y-k \right)}^{2}}={{r}^{2}} \\
& {{\left( x-\left( -4 \right) \right)}^{2}}+{{\left( y-\left( 3 \right) \right)}^{2}}={{\left( 3\sqrt{2} \right)}^{2}} \\
& {{\left( x+4 \right)}^{2}}+{{\left( y-3 \right)}^{2}}=9\cdot 2 \\
& {{\left( x+4 \right)}^{2}}+{{\left( y-3 \right)}^{2}}=18
\end{align}$
The equation of the circle with center $\left( -4,3 \right)$ and radius $3\sqrt{2}$ is ${{\left( x+4 \right)}^{2}}+{{\left( y-3 \right)}^{2}}=18$.
