Question

what is the radius of the circle with the equation (x + 2)^2+(y - 3)^2 = 100?
a. 10
b. 5
c. 20
d. 4

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 of the circle and $r$ is the radius.

Step2: Compare given equation

Given $(x + 2)^2+(y - 3)^2 = 100$, we can rewrite it as $(x-(-2))^2+(y - 3)^2=10^2$.

Step3: Determine the radius

By comparing with the standard - form, we see that $r^2 = 100$, so $r = 10$.

Answer:

A. 10