The lady travelled from Naples along with Neruda and his wife on the same ship, but they had not seen each other on board. They invited her to have coffee at their table, and the author urged her to talk about her fantasies to surprise the poet. Pablo Neruda paid no attention, for he had announced that he did not believe in prophetic dreams from the very beginning. 'Only poetry is clairvoyant,' he said.
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 \(P,O,Q\).