Answer
Center of circle is $\left( -5,1 \right)$ and radius is $r=\sqrt{15}$
Work Step by Step
Standard equation of the circle is:
${{\left( x-h \right)}^{2}}+{{\left( y-k \right)}^{2}}={{r}^{2}}$ (equation - 1)
And equation of circle is,
${{\left( x+5 \right)}^{2}}+{{\left( y-1 \right)}^{2}}=15$ (equation - 2)
Now compare both the equations,
$\begin{align}
& {{\left( x+5 \right)}^{2}}+{{\left( y-1 \right)}^{2}}=15 \\
& {{\left( x-\left( -5 \right) \right)}^{2}}+{{\left( y-\left( 1 \right) \right)}^{2}}=\sqrt{15} \\
\end{align}$
Center coordinate of circle is $\left( h=-5,k=1 \right)$.
And radius of circle is $r=\sqrt{15}$.
To graph, we plot the points$\left( -5,4.873 \right)$,$\left( -5,-2.873 \right)$,$\left( -8.9,1 \right)$and $\left( -1.1,1 \right)$ which are, respectively, $\sqrt{15}$ units above, below, left and right of $\left( -5,1 \right)$.
