determine the equation of the circle graphed below. answer attempt 1 out of 2 submit answer

Explanation:

Step1: Recall circle - equation formula

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

Step2: Identify the center of the circle

From the graph, the center of the circle $(h,k)=(-3,-4)$.

Step3: Calculate the radius

The distance between the center $(-3,-4)$ and a point on the circle $(1, - 1)$ can be found using the distance formula $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $x_1=-3,y_1 = - 4,x_2=1,y_2=-1$. Then $r=\sqrt{(1+3)^2+(-1 + 4)^2}=\sqrt{4^2+3^2}=\sqrt{16 + 9}=\sqrt{25}=5$.

Step4: Write the equation of the circle

Substitute $h=-3,k=-4,r = 5$ into the standard - form equation. We get $(x+3)^2+(y + 4)^2=25$.

Answer:

$(x + 3)^2+(y + 4)^2=25$