Answer
$(x+5)^{2}+(y+1)^{2}=26$
Work Step by Step
Since the circle passes through the origin, we know that it contains the point $(0,0)$. We can use this fact to find the radius. We are given that the circle has a center of $C=(-5,-1)$, so we have:
$r=\sqrt{(0--5)^{2}+(0--1)^{2}}=\sqrt{(0+5)^{2}+(0+1)^{2}}=\sqrt{25+1}=\sqrt{26}$
So the equation is:
$(x+5)^{2}+(y+1)^{2}=(\sqrt{26})^2=26$
