Dr Sadao will be arrested on the charge of harbouring an enemy if somebody complains against him and discloses the secret.He, on humanitarian grounds as well as professional grounds, had tended a wounded war- prisoner which was officially a serious crime. However, he did not get punished for this offence as it was never revealed to anyone, except his wife, loyal but timid servants, and a General who was too self-obsessed with his own treatment.It was sure that he would never let the doctor leave him.
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 \(P,O,Q\).