The shape of a hanging chain between the points \((-a, b)\) and \(

(a, b)\) is such that the gravitational potential energy

\[V[y]=ho g \int_{-a}^{a} y \sqrt{1+y^{\prime 2}} d x\]

is minimized subject to the length of the chain remaining constant,

\[L[y]=\int_{-a}^{a} \sqrt{1+y^{\prime 2}} d x\]

Find the shape, \(y(x)\) of the hanging chain.