so, we know the center is at -1, -3, hmmm what's the radius anyway?
well, the radius will be the distance from the center to any point on the circle, it just so happen that we know -7, -5 is on it, thus
[tex]\bf ~~~~~~~~~~~~\textit{distance between 2 points}\\\\
\begin{array}{ccccccccc}
&&x_1&&y_1&&x_2&&y_2\\
% (a,b)
&&(~ -1 &,& -3~)
% (c,d)
&&(~ -7 &,& -5~)
\end{array}
\\\\\\
d = \sqrt{( x_2- x_1)^2 + ( y_2- y_1)^2}
\\\\\\
r=\sqrt{[-7-(-1)]^2+[-5-(-3)]^2}\implies r=\sqrt{(-7+1)^2+(-5+3)^2}
\\\\\\
r=\sqrt{36+4}\implies r=\sqrt{40}\\\\
-------------------------------[/tex]
[tex]\bf \textit{equation of a circle}\\\\
(x- h)^2+(y- k)^2= r^2
\qquad
center~~(\stackrel{-1}{ h},\stackrel{-3}{ k})\qquad \qquad
radius=\stackrel{\sqrt{40}}{ r}
\\\\\\\
[x-(-1)]^2+[y-(-3)]^2=(\sqrt{40})^2\implies (x+1)^2+(y+3)^2=40[/tex]
