The story ‘The Enemy’ is built on the pillars of selflessness, sense of duty, kindness and generosity. There have been many films and novels based on this theme. One such example is the film ‘My Name is Khan’, where the protagonist, with a sense of duty and generosity, goes to the flooded Georgia to save the lives of his friends, Mama Jenny, Joel and other natives. He selflessly works to save the town without thinking twice about the possible dangers to his own life.
How did Dr. Sadao plan the American prisoner’s escape? (The Enemy)
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 \(P,O,Q\).