To determine the center of a circle given by the equation [tex]\((x+9)^2 + (y-6)^2 = 10^2\)[/tex], we need to compare it with the standard form of a circle's equation:
[tex]\[
(x-h)^2 + (y-k)^2 = r^2
\][/tex]
In this standard equation:
- [tex]\((h, k)\)[/tex] represents the center of the circle.
- [tex]\(r\)[/tex] is the radius of the circle.
Comparing the given equation [tex]\((x+9)^2 + (y-6)^2 = 10^2\)[/tex] with the standard form:
- The term [tex]\((x+9)^2\)[/tex] indicates that [tex]\(x - (-9)\)[/tex] is squared, meaning [tex]\(h = -9\)[/tex].
- The term [tex]\((y-6)^2\)[/tex] indicates that [tex]\(y - 6\)[/tex] is squared, meaning [tex]\(k = 6\)[/tex].
Thus, the center of the circle is given by the coordinates [tex]\((h, k)\)[/tex], which are:
[tex]\[
(h, k) = (-9, 6)
\][/tex]
So the correct answer is:
[tex]\[
\boxed{(-9, 6)}
\][/tex]
