Question 1 - 24 marks Let y be a real constant with 2 1 for the parametric functional S[x, y] = dt 12 + 2 yay + 1 - May - ry) , 1>0, with the boundary conditions r(0) = y(0) =0, r(1) = R > 0 and y(1) = 0. (a) Show that the stationary paths of this parametric functional are given by the solutions of the equations d.x dy dy =2(c-xy) and Y + 2(d + Xx), ds ds ds ds where c and d are constants and s(t) = di Vi2 + 2yxy + yz. [12] (b) Show that dr 2 d.x dy dy 2 = 1. [2] ds + 27 is ds + ds