Answer
$\\(x+3)^2+(y+1)^2=3$
Work Step by Step
RECALL:
The standard form of the equation of a circle with a center of $(h, k)$ and a radius of $r$ units is:
$(x-h)^2 + (y-k)^2 = r^2$
The given circle has its center at $(-3, -1)$ and a radius of $\sqrt3$ units.
Use the standard form above where $h=-3$, $k=-1$, and $r=\sqrt3$ to obtain:
$[x-(-3)]^2 + [y-(-1)]^2 =(\sqrt3)^2
\\(x+3)^2+(y+1)^2=3$