When the American war- prisoner came to consciousness and realized that he was saved by a Japanese family, he feared that he would be soon handed over to the army. However, as he noticed the amount of concern and care given to him by the family, he understood that he was in safe hands. He knew that although he was a threat to the doctor’s family, his own life might be saved there.War is man-made.The soldier was hired to fight in the war.He was not at all interested to join it once more.But he was helpless. Burdened with gratitude towards the family, he ultimately decides to comply with what the doctor planned for him - the escape.
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 \(P,O,Q\).