A woman with the snake ring on her index finger was three chairs away when Paulo Neruda was eating at a table. He noticed she was staring at him, and he instantly informed the author that somebody behind was looking at him. So, when the author glanced over his shoulder, it was true. He found a fearless woman in an old-fashioned felt hat and a purple scarf, eating without haste and staring at him. He could recognize her right away. She had grown old and fat, but it was Frau Frieda, with the snake ring on her index finger, staring at Pablo Neruda.
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 \(P,O,Q\).