Frank was an Irish sailor and a man whom Eveline loved and admired. She loved him so much that she wanted to elope with him and lead a respectful life. He was a very kind and open-hearted man who wished to marry Eveline. But Eveline's father had found out about the affair and was against her wish and had forbidden her from saying anything to him. Hence, Eveline's father did not like him and quarrelled with him about their affair.
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 \(P,O,Q\).