Question

what is the radius of the circle $x^{2}+y^{2}-81 = 0$? simplify any fractions.

Explanation:

Step1: Rewrite to standard circle form

Rearrange the given equation to match the standard form of a circle centered at the origin, $x^2 + y^2 = r^2$.
$$x^2 + y^2 = 81$$

Step2: Solve for radius $r$

Take the positive square root of the right-hand side, since radius is positive.
$$r = \sqrt{81} = 9$$

Answer:

9