Well, here is the complete, static, problem:

An oilrig is floating on the surface. One of the mooring lines keeping the rig in place has an attached buoy at some point, in order to move the touchdown point (where the line meets the seabed) further away from the rig.

The curve will look something like this: http://www.globalmaritime.com/navalarch/mooring1.png where the discontinouation is the point where the upwards buoyancy force from the buoy is acting.

M in the equation is the weight of the line in N/m, and D and R is the horizontal and vertical distances from the rig (fairlead) to the buoy. However, I belive there must be a simpler approach than what I have attempted. (e.g. by using line distance S, instead of D and R)

Basically, I need to find an expression for the slope of the line, given that i know the line tension at the rig (fairlead), the buoyancy force of the buoy, the line weight M, the point on the line where the buoy is attached, and the total length of the line.

Think that's it

Dan