Answer
$x^{2}+(y-290)^{2}=67,600$
Work Step by Step
The diameter is 520 ft, so the radius is $r=260$ ft.
If the center was 260 ft above the origin, 520 ft would be the highest point.
The maximum height is 550, however, the center is raised, at
(260+30) ft above the origin, on the y-axis, at the point
$(h,k)=(0,290)$
The standard form of an equation of a circle with radius $r$ and center $(h,k)$ is
$(x-h)^{2}+(y-k)^{2}=r^{2}$
$x^{2}+(y-290)^{2}=260^{2}$.
$x^{2}+(y-290)^{2}=67,600$
