To find the center of the circle given by the equation \((x+5)^2 + (y-7)^2 = 36\), we need to identify the standard form of a circle's equation, which is:
[tex]\[
(x-h)^2 + (y-k)^2 = r^2
\][/tex]
Here, \((h, k)\) represents the center of the circle and \(r\) represents the radius.
In the given equation:
[tex]\[
(x+5)^2 + (y-7)^2 = 36
\][/tex]
we should match it to the standard form. Comparing the two equations, we observe that:
- \( (x-h)^2 \) matches with \((x+5)^2\), which indicates that \( h = -5 \). This is because \((x - (-5)) = (x + 5)\).
- \( (y-k)^2 \) matches with \((y-7)^2\), which indicates that \( k = 7 \).
Therefore, the center \((h, k)\) of the circle is:
[tex]\[
(-5, 7)
\][/tex]
So, the center point of the circle is [tex]\(\boxed{(-5, 7)}\)[/tex].
