Dr Sadao will be arrested on the charge of harbouring an enemy if anyone complains against him.However,he knew that they would be arrested if they sheltered a white man in their house. The wounded man was a prisoner of war who had escaped with a bullet on his back. Since Japan was at war with America, harbouring an enemy meant being a traitor to Japan.In that case he might be treated as a traitor despite his compassion for his fellow beings.
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 \(P,O,Q\).