Parabolic motion to reach certain point

Aug 2010
434
174
https://ibb.co/n57i8y


what is the formula to specify the correct v0y and v0x to reach the red point and x max?
There are an infinite number of different ways to cover the same parabolic path. If we take the "horizontal speed" to be constant, then we can write \(\displaystyle x= v_{0x}t\) and \(\displaystyle y= -(g/2)t^2+ v_{0y}t\). But I see two different "red points". y will be 0 at both t= 0 and \(\displaystyle t= \frac{2v_{0y}}{g}\). At that point x is \(\displaystyle x_{max}= \frac{2v_{0x}v_{0y}}{g}s\)