Catenary Curve of Length S, hanging from points A and B

This is the construction of the catenary curve y=a*cosh((x-c)/a)+b of length s (like a chain of length s), hanging on points A and B. The constructon follows the wikipedia article on catenary curves, i.e. first solve for a by solving sqrt(s^2-v^2)=2a*sinh(h/(2a)), then solve for b and c. View CAS to see details.