Dr Margolin realised that something was wrong when he noticed that his wallet was missing from his shirt pocket and he was not sure how and where he had lost his wallet. He also couldn’t understand that his true love, Raizel, being present at the wedding, looked too young, and he was in a dilemma that she might be her daughter, who was trying to mock him. All these events led Dr Margolin to a confused state of mind.
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 \(P,O,Q\).