Question

choose the equation of a circle with radius 8 and center (3, - 5). choose the correct answer below. a. (x - 3)^2+(y + 5)^2 = 8 b. (x - 3)^2+(y + 5)^2 = 64 c. (x + 3)^2+(y - 5)^2 = 8 d. (x + 3)^2+(y - 5)^2 = 64

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 given values

The center of the circle is $(3,-5)$, so $h = 3$ and $k=-5$. The radius $r = 8$.

Step3: Substitute values into the formula

Substitute $h = 3$, $k=-5$, and $r = 8$ into $(x - h)^2+(y - k)^2=r^2$. We get $(x - 3)^2+(y+5)^2=64$.

Answer:

C. $(x - 3)^2+(y + 5)^2=64$