The doctor tried his best to save the injured soldier as a part of his duty. But the ultimate question was what to do next. It cannot be said that he betrayed his country as he told the truth to the General. However ,when he noticed that the soldier was to be killed not for the benefit of the country but only to save the doctor’s life, he decided to help him flee. In such a situation, the doctor's final solution to the problem was the best possible one.
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 \(P,O,Q\).