To determine the center of the circle given the equation [tex]\((x-11)^2 + (y-9)^2 = 225\)[/tex], we need to compare it to the standard form of a circle's equation.
The standard equation of a circle is:
[tex]\[
(x - h)^2 + (y - k)^2 = r^2
\][/tex]
Where [tex]\((h, k)\)[/tex] is the center of the circle, and [tex]\(r\)[/tex] is the radius.
Given the equation:
[tex]\[
(x - 11)^2 + (y - 9)^2 = 225
\][/tex]
We can see that it matches the standard form, with the following components identified:
- [tex]\(h = 11\)[/tex]
- [tex]\(k = 9\)[/tex]
- [tex]\(r^2 = 225\)[/tex]
So, the center of the circle [tex]\((h, k)\)[/tex] is:
[tex]\[
(11, 9)
\][/tex]
Therefore, the center of the circle is:
[tex]$
\boxed{11}
\boxed{9}
$[/tex]
