Question

what is the center of the circle $x^{2}+y^{2}-9 = 0$? simplify any fractions. (\boxed{}, \boxed{})

Explanation:

Step1: Recall circle standard form

The standard equation of a circle is $(x-h)^2 + (y-k)^2 = r^2$, where $(h,k)$ is the center, and $r$ is the radius.

Step2: Rewrite given equation

Rearrange $x^2 + y^2 - 9 = 0$ to match the standard form:
$$(x-0)^2 + (y-0)^2 = 9$$

Step3: Identify center coordinates

Compare with the standard form: $h=0$, $k=0$.

Answer:

$(0, 0)$