Eveline loved Frank a lot, and when she decided to elope with Frank and marry him, it was not easy for her as all her memories of childhood, happy days, mother and siblings flashed in front of her eyes like a movie. She felt sentimental about the memories with her brothers Harry and Ernest, who had left her house. The music played by the organ player reminded her of the day her mother died.On the other side, she wanted to run away from her father's cruelty and start a new respectful life with Frank in Buenos Aires. However, the promises she had given to her mother were that she would keep the house together as long as she could. The flash of memories kept haunting her, which did not let her go away with Frank.
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 \(P,O,Q\).