Question

what is the center of the circle with the equation $(x - 9)^2+(y + 4)^2 = 121$?
a. $(-9,-4)$
b. $(9,4)$
c. $(9,-4)$
d. $(-9,4)$

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: Identify $h$ and $k$ values

For the given equation $(x - 9)^2+(y + 4)^2=121$, we can rewrite $(y + 4)^2$ as $(y-(-4))^2$. Comparing with the standard - form, we have $h = 9$ and $k=-4$.

Answer:

C. $(9,-4)$