Let x = x(u, v) = u + v^2, and y = y(u, v) = u^2 + v^4.

(a). Find out where the Jacobian of the transformation equals 0, and find the chambers in the u-v plane where the Jacobian is positive and the chambers where it is negative.

(b). Find the curves in the x-y plane that correspond to the rays in the u-v plane where the Jacobian equals 0. (One of the curves is only half a curve!)

(c). As you go counterclockwise about the origin in the u-v plane, describe the corresponding motion in the x-y plane, using your answer to part (a).