Problem 4 Construct a transformation (F : R? - R?) that maps the ellipse in the ry-plane given by 512 + 5y' - 8xy = 9 to the unit circle in the st-plane given by $2 + 12 = 1. Determine the area of the ellipse by using the change of variables formula. Hint: Construct the transformation in two steps. First apply a map that puts the ellipse in standard form. Then apply a second map that re-scales the ellipse into a circle of radius 1