Move/rotate until lowest point of curve hit a specific point.

Hi all,

I have a curve, which is my main object in the shape. The curve changes in shape with a bunch of parameters (it's not a linear curve). The first point must always hit X0 with a varying Y. What I need to do is to move and rotate the curve when the shape changes so the starting point remains at X0 and lowest point of the curve always hit X1000,Y0.
The curve starting point should automatically move along the Y-axis and the curve be rotated up/down to get the lowest point where it's supposed to be (1000 clicks away).

In the attached image I'm trying to explain what I'm after. The two sliders in the bottom should not be there, their values should be generated automatically.

I'm too new at GH and I'm stuck. Any ideas?