Dr Sadao Hoki was an eminent Japanese surgeon and scientist. He had spent eight valuable years of his youth in America to learn everything of surgery and medicine. He was trying to bring perfection to medical science and discover a drug which would·heal wounds entirely . Dr Sadao's house was built on rocks well above a narrow beach that was outlined with bent pines. It was near the Japanese coast.
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 \(P,O,Q\).