Dr Sadao and Hana knew that their decision to save the enemy soldier would be questioned by everyone. However, they firmly followed their sense of duty. For Dr Sadao this sense of duty came from the profession he was in; but for Hana, the duty was purely humanitarian. From bearing the defiance from her domestic staff to being forced to do all the chores of house-hold herself, she does all with grace and dignity. Hana’s loving, considerate and sympathetic nature shines out. She washed and fed the soldier although it was not her job. Her care helped recuperate the soldier fast. It is also apparent from the story that she respected her husband, and as a sense of duty towards him, did the needful. This explains why she, even after feeling sick, comes back to the room and readily does whatever is told by her husband during the operation.
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 \(P,O,Q\).