Through this satirical story the author has rightly portrayed how human beings have subjected innocent animals to untold torture and death, merely to fulfill their own whims and fancies. The maharaja’s indiscriminate killing of tigers led to their extinction in some states, but the maharaja was oblivious to the grave consequences his action was leading to. In order to prove an astrologer wrong the maharaja went on a killing spree proving his dominance over the hapless animals.He wished to show his superiority as a human being and exercised his power to kill hundred unlucky tigers.
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 \(P,O,Q\).