Finding the constant in a catenary equation

[CartoonKid]

Can somebody teach me a better way to solve the equation of catenary cable to find the value of c? If there is no other better alternative, can you tell me how to estimate a value for the trial and error method.

Thanks

 

[CartoonKid]

Do you understand what c I am referring to? I don't know if the sign convention used by me is the same as you. It is the imaginary point located below the lowest point of a catenary cable, which acts as origin. Please tell me should you need further explanation.

Thanks