Question

choose the equation of a circle with radius 6 and center (3, - 4).
choose the correct answer below.
a. (x + 3)^2+(y - 4)^2 = 36
b. (x + 3)^2+(y - 4)^2 = 6
c. (x - 3)^2+(y + 4)^2 = 36
d. (x - 3)^2+(y + 4)^2 = 6

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 values of $h$, $k$, and $r$

Given that the center is $(3,-4)$, so $h = 3$ and $k=-4$. The radius $r = 6$, and $r^2=36$.

Step3: Substitute values into formula

Substitute $h = 3$, $k=-4$, and $r^2 = 36$ into the equation $(x - h)^2+(y - k)^2=r^2$. We get $(x - 3)^2+(y+4)^2=36$.

Answer:

C. $(x - 3)^2+(y + 4)^2=36$