Answer
$(x+1)^2+(y+2)^2=1$
Work Step by Step
RECALL:
The standard form of a circle's equation is given as:
$(x-h)^2+(y-k)^2=r^2$
where $r$ = radius and $(h, k)$ is the center.
Thus, a circle with center at $(-1, -2)$ and $r=1$ has the equation:
$[(x-(-1)]^2+[y-(-2)]^2=1^2
\\(x+1)^2+(y+2)^2=1$