Dr Sadao and Hana will help the man.They had found an unconscious wounded war prisoner who posed a huge threat to their own safety. However, Dr Sadao decided to go with his gut feeling and operate on him. He saved his life even though it was for the time being. Though half heartedly, both took good care of the patient’s health and other needs. Hana even washed and fed him with her own hands. Although they knew that they would have to hand him over to the army sooner or later, they did their best to help the injured man.
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 \(P,O,Q\).