Optimal control: Maximum area under the curve

Question

Suppose we are given two points P = ($2$,$0$), and Q($4$,$0$). I want to find the curve of length 6 connecting P to Q, which encloses the largest area above the horizontal axis. The constraint for this problem is $6 = \int_{2}^{4}\sqrt{1+\dot{y}^2}dx$ and our objective is $J = -\int_{2}^{4}y(x)dx$. At this point I should construct the Hamiltonian but I have no idea how to proceed.