The only occasion when Sophie got to see Danny Casey in person was when the family went to watch United on Saturday. Sophie, her father and little Derek went down near the goal. Geoff went with his mates higher up. United won two-nil. Her idol Casey drove in the second goal. She saw the Irish genius going round two big defenders on the edge of penalty area. He beat the hesitant goal keeper from a dozen yards. Sophie glowed with pride.
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 \(P,O,Q\).