Frau Frieda comprehends her dreams and predicts the fate of the family members, which earned her a job in Viennese in a very religious family. She came across the author while on this job. When the author tries to ask about her whereabouts, to which she replied, "I sell my dreams". Thus, the author was made to believe in the prophetic ability of Frau Frieda when she advised him to leave Viennese five years ago. But actually, the author reveals that he had to leave Viennese for some other reasons, not because she had a bad dream about him and advised him to leave Viennese. The author feels she's just using tricks to continue her job of selling dreams to liveliness.
A racing track is built around an elliptical ground whose equation is given by \[ 9x^2 + 16y^2 = 144 \] The width of the track is \(3\) m as shown. Based on the given information answer the following: 
(i) Express \(y\) as a function of \(x\) from the given equation of ellipse.
(ii) Integrate the function obtained in (i) with respect to \(x\).
(iii)(a) Find the area of the region enclosed within the elliptical ground excluding the track using integration.
OR
(iii)(b) Write the coordinates of the points \(P\) and \(Q\) where the outer edge of the track cuts \(x\)-axis and \(y\)-axis in first quadrant and find the area of triangle formed by points \(P,O,Q\).