Let x = t. Then the orange line consists of all points (t, t, 0)

The length of the orange line segment from (0, 0, 0) to (85, 85, 0) is

The equation of a parabola with it's vertex at (0, 0, 30) is

where s is the unit on the orange line when x and y increases by 1. So

Determine the value of a if p = 0 at (85, 85, 0).

I've got

So the equation of the parabola is