Not that he faced no dangers. There were times when the bullet missed its mark, the tiger leapt upon him and he fought the beast with his bare hands. Each time it was the Maharaja who won. At another time he was in danger of losing his throne. A high-ranking British officer visited Pratibandapuram. He was very fond of hunting tigers. And fonder of being photographed with the tigers he had shot.
(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 \(P,O,Q\).