Read the following passage and answer the questions given below.

In an elliptical sport field the authority wants to design a rectangular soccer field with the maximum possible area. The sport field is given by the graph of `(x^(2))/(a^(2)) + (y^(2))/(b^(2)) = 1` .
If the length and the breadth of the rectangular field be 2x and 2y respectively, then find the area function in terms of x.