As the hour of her departure with Frank neared, Eveline suddenly got restless and turned pale out of fear, whether she was doing right or wrong. She also felt depressed and cried out of anguish. She also prayed to God to direct her to the right path and perform her duties in the right way. Thus, God led her from not moving away from her duties and skipped the idea of eloping 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 \(P,O,Q\).