Question

what is the equation of a circle with center (-4, 7) and radius 6?
a. (x - 4)^2+(y + 7)^2 = 36
b. (x - 4)^2+(y + 7)^2 = 6
c. (x + 4)^2+(y - 7)^2 = 6
d. (x + 4)^2+(y - 7)^2 = 36

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

Given the center $(-4,7)$ and radius $r = 6$, we have $h=-4$, $k = 7$, and $r = 6$.

Step3: Substitute the values into the formula

Substitute $h=-4$, $k = 7$, and $r = 6$ into $(x - h)^2+(y - k)^2=r^2$. We get $(x-(-4))^2+(y - 7)^2=6^2$, which simplifies to $(x + 4)^2+(y - 7)^2=36$.

Answer:

D. $(x + 4)^2+(y - 7)^2=36$