Answer
Center of circle is $\left( -1,-3 \right)$ and radius is $r=7$.
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.
And equation of the circle is ${{\left( x+1 \right)}^{2}}+{{\left( y+3 \right)}^{2}}=49$ (equation - 2)
Now compare the standard equation with equation of the circle.
$\begin{align}
& {{\left( x+1 \right)}^{2}}+{{\left( y+3 \right)}^{2}}=49 \\
& {{\left( x-\left( -1 \right) \right)}^{2}}+{{\left( y-\left( -3 \right) \right)}^{2}}={{\left( 7 \right)}^{2}} \\
\end{align}$
Center coordinate of circle is $\left( h=-1,k=-3 \right)$.
And radius of circle is $r=7$.
To graph, we plot the points$\left( -1,4 \right)$, $\left( -1,-10 \right)$, $\left( -8,-3 \right)$, and $\left( 6,-3 \right)$ which are, respectively, 7 units above, below, left and right of $\left( -1,-3 \right)$.
