Dr Margolin’s past was a blend of recognition and sadness. As a child, he was lauded as a prodigy. He always felt he was a failure. Everyone in their home town assumed he would grow up to be a genius in his childhood days, but he faced difficulties. The loss of his true love, Raizel, affected his mental health, and he lost complete faith in humanity. His family had been tortured, burned and gassed. He also suffered from fear of death. All these incidents shaped Dr Margolin’s existing state of mind. However, on the professional front, he was successful and had a promising career. He had an office in West End Avenue and wealthy patients. He was highly regarded and respected by his close associates and everyone else.
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 \(P,O,Q\).