Answer
$$ x^2+y^2=106$$
Work Step by Step
Since the center is at the origin, we use the distance formula to find that the radius must be:
$$\sqrt{\left(5-0\right)^2+\left(9-0\right)^2}=\sqrt{106}$$
Thus, it follows:
$$x^2+y^2=r^2 $$
$$ x^2+y^2=106$$
