Question

which radius corresponds to the circle with the equation $(x + 5)^2+(y - 1)^2 = 121?
a. 13
b. 12
c. 121
d. 11

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 $(x + 5)^2+(y - 1)^2=121$, we can rewrite it as $(x-(- 5))^2+(y - 1)^2=121$. Since $r^2 = 121$.

Step3: Solve for the radius $r$

Take the square - root of both sides of the equation $r^2=121$. We get $r=\sqrt{121}=11$ (we consider the positive value of $r$ because the radius is a non - negative quantity).

Answer:

D. 11