When talking about his kid, Hagberd seemed to be optimistic that he would return home soon. She had pitifully attempted to cast doubt on that hope condemned to fail. Captain Hagberd gave her a horrific and unexpected reaction, and for a brief period, he appeared to be about to lose his mind. My youngster can't stay away from the sea, and there's nothing that can stop him from returning. His gaze began to stray. But the next day, Bessie humoured him in silence beside the fence, patiently listening.
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 \(P,O,Q\).