Write the standard form of the equation of the circle described below.
Center $(0,-1)$ passes through the point $(-1,-2)$

Step 1 ：The standard form of the equation of a circle is given by $(x-h{)}^2+(y-k{)}^2=r^2$, where $(h,k)$ is the center of the circle and $r$ is the radius.

Step 2 ：We know the center of the circle is $(0,-1)$, so $h=0$ and $k=-1$.

Step 3 ：We can find the radius by calculating the distance between the center of the circle and the point it passes through, which is $(-1,-2)$.

Step 4 ：Using the distance formula, we find that $r=\sqrt{2}$.

Step 5 ：Now that we have the radius, we can substitute the values of $h$, $k$, and $r$ into the standard form of the equation of a circle to get the equation of the given circle.

Step 6 ：Substituting the values, we get $(x-0{)}^2+(y+1{)}^2=2$.

Step 7 ：Final Answer: The standard form of the equation of the circle is $\boxed{{\displaystyle (x-0{)}^2+(y+1{)}^2=2}}$