A boy throws a ball at a constant speed V for every throw, show that no matter what angle alpha to the horizontal this boy throws the ball at, the ball cannot move beyond a certain curve in the xy plane. Find the equation of this curve. Model the ball as a particle and forget about air resistance.

This problem has been annoying me for a while now, I believe I have correctly derived all the equations of motion I can, I have the horizontal distance and the vertical distance, I eliminated time from both of these to obtain the path of the ball for a certain angle. I also have the maximum horizontal and vertical distance obtained for a certain angle. I thought to find the maximum distance from the boy that the ball will obtain I should square the horizontal and vertical distances, sum them, differentiate them with respect to t, solve for t for 0 and then substitute t back in, but that didn't get me very far.

Any ideas?

Edit: Apparently the answer is

but I can't see how to get there