Dr Margolin, son of a poor teacher of Talmud, was a self-taught man. In his childhood days, he was lauded as a prodigy. He studied Talmud and commentaries independently and could recite long passages of the Bible by himself. He also learnt algebra and geometry by himself. At the age of seventeen, he attempted a translation that led him to be considered a genius.
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 \(P,O,Q\).