Question

The equation of a circle is (x + 3)2 + (y + 5)2 = 8. Determine the coordinates of the center of the circle. ??

Answer 1

$\bf \textit{equation of a circle}\\\\ (x- h)^2+(y- k)^2= r^2 \qquad center~~(\stackrel{}{ h},\stackrel{}{ k})\qquad \qquad radius=\stackrel{}{ r} \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ (x+3)^2+(y+5)^2=8\implies [x-(\stackrel{h}{-3})]^2+[y-(\stackrel{k}{-5})]^2=(\stackrel{r}{\sqrt{8}})^2 \\\\[-0.35em] \rule{34em}{0.25pt}\\\\ ~\hfill \stackrel{center}{(-3,-5)}~\hfill$