Among the curves of given length $l$, at the upper half-plane, passing through the points $(-a, 0)$ and $(a, 0)$ , find the one that encloses the largest surface area together with the space $[-a,a]$.
I believe the answer for this problem is that there is no such curve because one can always find one another curve than encloses a larger surface area than the previous one. Until now, I have only minimized functionals and, thus, I have no clue from where to begin to prove my case in this problem. My questions are:
- Is my answer the right one?
- What can I do to solve this kind of problem?
I hope that I've been clear. Thanks in advance!!