Consider a string of fixed length l. One end is fixed at the point (x = a, y = 0), and the other end is fixed at the point (x = a, y = 0). You place the string in the x-y-plane such that it maximizes the area enclosed between the string and the x-axis. (a) Use the Euler-Lagrange equations (introducing a Lagrange multiplier ) to find the shape that the string should take. Sketch what it would look like. (b) What is the geometric meaning of in this problem? Write an equation that related , a and l. Hint: the correct equation is transcendental, and you do not have to solve it. The answer to part a is y = sqrt(^2 - (x + c)^2) + d, where c and d are just arbitrary constants. Thus, the shape of the string is a semicircle. Solve part b