He's still advertising for Harry Hagberd in the Sunday papers. He informed Bessie that these sheets had been read in far-flung corners of the globe. Simultaneously, he appeared to believe that his son was in England—so close to Colebrook that he would arrive ‘tomorrow.' Bessie, without committing herself to that position in so many words, maintained that in that circumstance, the cost of transportation was justified. It would be better if you spent that week half-crown on Captain Hagberd instead of advertising. Miss Bessie referred to his outbursts as tantrums. She aggressively shook her finger at him. Captain Hagberd's actions anger and disgust Bessie from time to time.
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 \(P,O,Q\).