Dr Margolin did not accept nor appreciate the kind of life the American Jewish community led. Jewish laws and customs were utterly distorted, according to him. He did not like their celebrations, and he felt annoyed and irritated. Those who had no regard for Jewishness wore skullcaps. He disliked Anglicised Yiddish, the Yiddishised English, the ear-splitting music and the unruly way of dance. He felt ashamed and did not like taking his wife to a wedding or any such gatherings.
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 \(P,O,Q\).