Question

the circle below is centered at the point (8, 4) and has a radius of length 4. what is its equation? a. (x - 4)^2+(y - 8)^2 = 4^2 b. (x - 4)^2+(y + 8)^2 = 4 c. (x + 8)^2+(y - 4)^2 = 16 d. (x - 8)^2+(y - 4)^2 = 16

Explanation:

Step1: Recall circle - equation formula

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

Step2: Identify values of $h$, $k$, and $r$

Given that the center is $(8,4)$ and the radius $r = 4$. Here, $h = 8$, $k = 4$, and $r^2=4^2 = 16$.

Step3: Substitute values into the formula

Substitute $h = 8$, $k = 4$, and $r^2=16$ into the equation $(x - h)^2+(y - k)^2=r^2$, we get $(x - 8)^2+(y - 4)^2=16$.

Answer:

D. $(x - 8)^2+(y - 4)^2=16$