The two characters Eveline liked and loved were her mother and Frank the most. Eveline's mother bore the torture inflicted upon her by her husband and took care of the complete family by providing all the comforts to her children. Frank was her very kind, manly, open-hearted lover, and he admired her very much. He was the only hope for her future, who would get her out of the problems she faced. She hated her father and Miss Gavan as they both used to criticise her and they had always been harsh towards her. Her father used to drink and humiliate her, whereas Miss Gavan always passed comments on her.
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 \(P,O,Q\).