Question

what is the standard form of the equation of the circle shown below? a $(x - 2)^2+(y - 2)^2 = 16$ b $(x + 2)^2+(y - 2)^2 = 16$ c $(x - 2)^2+(y + 2)^2 = 16$ d $(x + 2)^2+(y + 2)^2 = 16$

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: Determine center and radius from the graph (assume center is $( - 2,2)$ and radius $r = 4$)

Substitute $h=-2$, $k = 2$ and $r = 4$ into the formula. We get $(x-(-2))^2+(y - 2)^2=4^2$, which simplifies to $(x + 2)^2+(y - 2)^2=16$.

Answer:

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