Question

write an equation of a circle that is centered at (4, -7) with a radius of 6. a ((x - 4)^2 + (y + 7)^2 = 6) b ((x - 4)^2 + (y + 7)^2 = 36) 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 a circle's equation is $(x-h)^2 + (y-k)^2 = r^2$, where $(h,k)$ is the center and $r$ is the radius.

Step2: Substitute center $(4,-7)$

Substitute $h=4$, $k=-7$: $(x-4)^2 + (y-(-7))^2 = r^2$ simplifies to $(x-4)^2 + (y+7)^2 = r^2$.

Step3: Substitute radius $r=6$

Calculate $r^2 = 6^2 = 36$, so the equation is $(x-4)^2 + (y+7)^2 = 36$.

Answer:

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