Question

determine the equation of the circle graphed below.

Explanation:

Step1: Identify circle center

From the graph, the center $(h,k)$ is $(-5, -2)$.

Step2: Calculate radius length

Count horizontal/vertical distance from center to edge: from $x=-5$ to $x=0$ is 5 units, so $r=5$.

Step3: Use circle standard formula

The standard circle equation is $(x-h)^2+(y-k)^2=r^2$. Substitute $h=-5$, $k=-2$, $r=5$.
$$(x-(-5))^2+(y-(-2))^2=5^2$$
Simplify the signs and exponent:
$$(x+5)^2+(y+2)^2=25$$

Answer:

$\boldsymbol{(x+5)^2+(y+2)^2=25}$