write the equation of the circle graphed below.

Explanation:

Step1: Identify center coordinates

The center of the circle (red - dot) is at $(-2,-2)$. So, $h=-2$ and $k = - 2$ in the standard - form equation of a circle $(x - h)^2+(y - k)^2=r^2$.

Step2: Find the radius

The distance from the center $(-2,-2)$ to a point on the circle (blue - dot) which is at $(-1,-2)$ can be found using the distance formula $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $x_1=-2,y_1=-2,x_2=-1,y_2=-2$. Then $r=\sqrt{(-1+2)^2+(-2 + 2)^2}=\sqrt{1+0}=1$.

Step3: Write the equation of the circle

Substitute $h=-2,k=-2,r = 1$ into the standard - form equation $(x - h)^2+(y - k)^2=r^2$. We get $(x + 2)^2+(y + 2)^2=1$.

Answer:

$(x + 2)^2+(y + 2)^2=1$