4. Let T be the transformation x = u2 - v2, y = 2uv. (a) Show that the lines u = a in the uv-plane map to parabolas in the xy-plane that open in the negative x-direction with vertices on the positive r-axis. (b) Show that the lines v = b in the uv-plane map to parabolas in the ry-plane that open in the positive r-direction with vertices on the negative r-axis. (c) Evaluate J(u, v). (d) Use a change of variables to find the area of the region bounded by r = 4 - " and x = 4 - 1. (e) Use a change of variables to find the area of the curved rectangle above the r-axis bounded by r =4-12 16: 2=9-4, x = 4 - 1, and x = " - 16