Question

what is the equation of the circle?
a. (x + 3)^2+(y - 2)^2 = 8
b. (x - 3)^2+(y + 2)^2 = 8
c. (x + 3)^2+(y - 2)^2 = 16
d. (x - 3)^2+(y + 2)^2 = 16

Explanation:

Step1: Find the center of the circle

The center of the circle is at $(3,-2)$ from the graph.

Step2: Recall the standard - form of a circle equation

The standard - form of a circle equation is $(x - h)^2+(y - k)^2=r^2$, where $(h,k)$ is the center of the circle and $r$ is the radius. Here $h = 3$ and $k=-2$, so the equation starts as $(x - 3)^2+(y+2)^2=r^2$.

Step3: Determine the radius

Count the distance from the center $(3,-2)$ to a point on the circle, say $(7,-2)$. The distance $r = 4$ (since $|7 - 3|=4$). Then $r^2=16$. So the equation of the circle is $(x - 3)^2+(y + 2)^2 = 16$.

Answer:

D. $(x - 3)^2+(y + 2)^2 = 16$