There have been a few instances of game hunting in the present times. Even the
affluent have been involved in instances that illustrate the callousness of human beings
towards wildlife.
Salman Khan – Black Buck poaching case.
Nawab Mansoor Ali Khan Pataudi - Antelope case.
Salman Khan is a Bollywood celebrity and is fond of game hunting.He poached
three Chinkaras in two separate incidents.Black Buck is an endangered species.Despite
knowing it Salman killed them.A case was lodged against him but he was acquitted.
Nawab Pataudi,the great cricketer, was also in the news for killing the rare species of
antelopes.
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 \(P,O,Q\).