Consider a massive string of constant linear mass density and length L whose endpoints are fixed

Consider a massive string of constant linear mass density μ and length L whose endpoints are fixed at A (x = 0, z = z0) and B (x = a, z = z1). The string lies in the vertical plane (x, z), and it is in the gravitational field, oriented along the vertical z axis. Determine the shape of the string at equilibrium. (Of course, we assume that

(z1 − z0)2 + a2 ≤ L2.)