check the picture below.
you can pretty much, without having to use the distance formula, see the diameter is 6 units long, thus the radius is half that or 3 then.
now, without having to use the midpoint formula, if we move from either endpoint inwards 3 units, we'll end up at the center, -5 -3, is just -8, so the center will be at -8, -3.
[tex]\bf \textit{equation of a circle}\\\\
(x-{{ h}})^2+(y-{{ k}})^2={{ r}}^2
\qquad
center~~(\stackrel{-8}{{{ h}}},\stackrel{-3}{{{ k}}})\qquad \qquad
radius=\stackrel{3}{{{ r}}}
\\\\\\\
[x-(-8)]^2+[y-(-3)]^2=3^2\implies (x+8)^2+(y+3)^2=9[/tex]
