Quote - For the hyperbolic cosine I have no idea, but I would expect it to be similar.

The problem for a Catenary {y = a cosh(x / a)} is that it's easy to find a for a given length of chain when the end points are the same height, if they are at different heights you have a second unknown, where the lowest point of the chain is relative to the ends (in the equal height case this is in the middle and is a special case).