Captain Hagberd and old Mr. Carvil are both irritable people who have a tendency to overreact to situations because their ability to deal with them is limited. On the same boat but in a different situation, Captain Hagberd calls Bessie when he wants something, shouting loudly like he is out of control, and old Mr Carvil, a fat blind man who had given himself up to a very lust of laziness, calls Bessie when he wants something, shouting loudly like he is out of control.
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 \(P,O,Q\).