Sophie liked her brother Geoff, more than anybody else because he was not in the habit of talking much and remained lost in his own thoughts. She envied his silence and thought that he had access to an unknown world. She wanted to be a part of that world where she fancied herself wearing glamorous clothes and being welcomed by everyone. For Sophie, Geoff symbolised liberty from the monotonous and colourless life they had been living.
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 \(P,O,Q\).