The poet uses the ‘Hindered Flags’ image to portray the beauty of flowers that stand on their stems with petals full of aroma having not bloomed fully. But, to dance like a tree, they have to bloom fully. So, before they could bloom, they have to slit open the tough green calyx. Hence, the ‘Hindered Flags’ represents flowers that have not bloomed fully.
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 \(P,O,Q\).