To determine the center of the circle represented by the equation [tex]\((x + 9)^2 + (y - 6)^2 = 10^2\)[/tex], it is helpful first to recall the standard form of the equation of a circle:
[tex]\[
(x - h)^2 + (y - k)^2 = r^2
\][/tex]
Here, [tex]\((h, k)\)[/tex] is the center of the circle, and [tex]\(r\)[/tex] is the radius.
Given the equation:
[tex]\[
(x + 9)^2 + (y - 6)^2 = 10^2
\][/tex]
we can compare this with the standard form:
- The term [tex]\((x + 9)^2\)[/tex] can be written as [tex]\((x - (-9))^2\)[/tex], indicating that [tex]\(h = -9\)[/tex].
- The term [tex]\((y - 6)^2\)[/tex] is already in the appropriate form [tex]\((y - k)^2\)[/tex], indicating that [tex]\(k = 6\)[/tex].
Therefore, the center of the circle is:
[tex]\[
(-9, 6)
\][/tex]
So, the correct answer is [tex]\((-9, 6)\)[/tex].
