Pabola Neruda, a friend of the author, had come to Spain for the first time. The author compares Neruda to a Renaissance pope because Neruda behaviour was that of a childish manner. He walked through the crowd like an invalid elephant. Whenever he watched something, his mind had a child's curiosity of its inner workings. For the author, the world appeared to him as a substantial wind-up toy. However, the author compared Neruda to a Renaissance pope as he was insatiable and refined. Thus, the author could not imagine anyone closer to the idea one has of a renaissance pope other than Neruda.
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 \(P,O,Q\).