Eveline remembered the organ player's appearance as the street organ that played the night before her mother's death. When Eveline decided to leave the house, the good old memories with her siblings, the promises she had given to her mother that she would take care of her family and would never get separated all flashed in front of her eyes like a movie. These instances held her back to fulfil her duties and stopped her from going away with her beloved 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 \(P,O,Q\).