To find the center of the circle given by the equation [tex]\( x^2 + y^2 = 64 \)[/tex], we need to recognize the standard form of a circle's equation. The general form of a circle's equation is:
[tex]\[ (x - h)^2 + (y - k)^2 = r^2 \][/tex]
Here, [tex]\((h, k)\)[/tex] represents the center of the circle, and [tex]\(r\)[/tex] is the radius.
In the given equation [tex]\( x^2 + y^2 = 64 \)[/tex], we can compare it to the general form:
1. [tex]\( (x - 0)^2 + (y - 0)^2 = 64 \)[/tex]
From this comparison, we see that [tex]\( h = 0 \)[/tex] and [tex]\( k = 0 \)[/tex]. Therefore, the center of the circle is at [tex]\((0,0)\)[/tex].
So, the answer is:
[tex]\[ \boxed{(0,0)} \][/tex]
