Question

what is the radius of the circle with the equation $(x + 3)^2+(y - 2)^2 = 36?
a. 9
b. 6
c. 3
d. 12

Explanation:

Step1: Recall circle - equation formula

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

Step2: Compare given equation with standard form

Given $(x + 3)^2+(y - 2)^2=36$, we can rewrite it as $(x-(-3))^2+(y - 2)^2 = 36$. Since $r^2=36$.

Step3: Solve for $r$

Take the square - root of both sides of the equation $r^2 = 36$. We get $r=\sqrt{36}=6$ (we consider the positive value of $r$ because the radius is a non - negative quantity).

Answer:

B. 6