Mr Lamb is an old man with a tin leg. His real leg was blown off years ago during the war. He lives all alone in his house. There is a garden near the house. It has ripe crab apples looking orange and golden in colour. Mr Lamb is sitting in his garden when Derry climbs over the garden wall to get into his garden. Though the gate is open, the boy does not use it.
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 \(P,O,Q\).