determine the equation of the circle graphed below.\nanswer\nattempt 1 out of 2\nsubmit 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 is $(-4,-5)$, so $h=-4$ and $k = - 5$.

Step3: Calculate the radius

The radius $r$ is the distance between the center $(-4,-5)$ and a point on the circle, say $(0,-3)$. Using the distance formula $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$, we have $r=\sqrt{(0+4)^2+(-3 + 5)^2}=\sqrt{4^2+2^2}=\sqrt{16 + 4}=\sqrt{20}=2\sqrt{5}$.

Step4: Substitute values into the circle - equation formula

Substitute $h=-4$, $k=-5$, and $r = 2\sqrt{5}$ into $(x - h)^2+(y - k)^2=r^2$. We get $(x + 4)^2+(y + 5)^2=(2\sqrt{5})^2$. Simplifying, we have $(x + 4)^2+(y + 5)^2 = 20$.

Answer:

$(x + 4)^2+(y + 5)^2=20$