Catenary equation given 2/3 points
I'm working on a research about catenaries and its use related to architectural and structural problems, something sort of interesting. And I just came across a really unexpected problem.
The thing is that I'm including some pics on catenaries (Gaudi, St Paul's Cathedral, St Louis Gateway arch...) and it would be great to draw their catenaries on the pics and describe their equations. The thing is catenary equation is (I'm working on arches, so that's why the minus sign; and they are simmetrical, nothing-weird curves):
y(x) = b - a*cosh(x/a)
(okay there should be one more argument, y(x) = b - a*cosh(x/a+c))
How do you get software like Maple / Derive solve such a system of equations? I have pics, so I can make up any x-y value correlation, but they simply come up with unsatifactory answers (undefine, floating point)... I guess I'm looking for an approximation or something. Don't really know, I have never worked with these stuff before. Really, any help would be greatly appreciated, really! this is driving me insane, and it must be easy.