To determine the center of the circle from its equation, let's first recall the standard form of a circle's equation:
[tex]\[
(x - h)^2 + (y - k)^2 = r^2
\][/tex]
In this equation, [tex]\((h, k)\)[/tex] represents the center of the circle and [tex]\(r\)[/tex] is the radius.
Given the equation of the circle:
[tex]\[
(x - 3)^2 + (y - 6)^2 = 64
\][/tex]
We can see that this equation matches the standard form, where:
- [tex]\(h = 3\)[/tex]
- [tex]\(k = 6\)[/tex]
Therefore, the center of the circle is the point:
[tex]\[
(3, 6)
\][/tex]
So, the correct choice is:
A. [tex]\((3, 6)\)[/tex]
