Whenever Dr Margolin took Gretl to a wedding or Bar Mitzvah, he felt ashamed. Even though she was born a Christian, Dr Margolin could see that American Judaism was a mess. At least this time, he would forgive himself for the trouble of making excuses to her. So, Dr Margolin does not particularly want his wife to accompany him to weddings or parties.
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 \(P,O,Q\).