The royal infant grew up to be the king of Pratibandapuram who was obsessed with the idea of killing one hundred tigers. He wanted to do so to disprove the prophecy which said that his death would come from the hundredth tiger. This made him kill all the tigers of Pratibandapuram. He even married for the sake of this ambition. He came to be known as the Tiger King.
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 \(P,O,Q\).