To determine the center of a circle represented by the equation [tex]\((x + 9)^2 + (y - 6)^2 = 10^2\)[/tex], we need to compare it to the standard form of a circle's equation, which is:
[tex]\[
(x - h)^2 + (y - k)^2 = r^2.
\][/tex]
In this standard form:
- [tex]\((h, k)\)[/tex] is the center of the circle.
- [tex]\(r\)[/tex] is the radius of the circle.
Given the equation [tex]\((x + 9)^2 + (y - 6)^2 = 10^2\)[/tex], we observe the following:
- The term [tex]\((x + 9)\)[/tex] can be rewritten in the form [tex]\((x - (-9))\)[/tex]. This translation means that [tex]\(h = -9\)[/tex].
- The term [tex]\((y - 6)\)[/tex] already matches the form [tex]\((y - k)\)[/tex], indicating that [tex]\(k = 6\)[/tex].
Therefore, the center of the circle is [tex]\((h, k)\)[/tex], which translates to:
[tex]\[
(h, k) = (-9, 6).
\][/tex]
So, the correct answer is [tex]\((-9, 6)\)[/tex].
