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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 x-axis. (b) Show that the lines v = b in the uv-plane map to parabolas in the xy-plane that open in the positive x-direction with vertices on the negative x-axis. (c) Evaluate J(u, v). (d) Use a change of variables to find the area of the region bounded by x = 4- 16 and x = 4- - 1. (e) Use a change of variables to find the area of the curved rectangle above the x-axis bounded by x=4-42 16 , *= 9 - 32 4 - 1, and x = 64 - 16