Equation of a Circle

It's time to play golf! Unfortunately for you, it's a windy day and the first hole of the course has a water hazard.

You place down your tee and analyze the surroundings, trying to determine whether you will hit your ball in the water. You place your tee on the line $x = 400$ yards, and predict that hitting the ball with your driver will cause the ball's path to follow the parabola $g(x) = \frac{13}{2250}(x - 250)^2 - 30.$

The lake you are trying to avoid has equation

$$(x - 250)^2 + (y + 30)^2 = 625.$$

To avoid landing in it, you try to move your tee upward (along the line $x = 400$). If the trajectory of the ball is such that it will always land when $x = 250,$ what is the smallest distance you can move your tee upward to avoid the lake?