To get the required number of tigers to kill, the Maharaja will ask his dewan to find a suitable girl for him to marry. A suitable girl for matrimonial alliance should be the one who would not only come from a royal family but also would belong to a state with a large tiger population. As Pratibandapuram had no more tigers left, a province that belonged to his father-in-law would certainly provide him with an opportunity to kill more tigers and reach his aim of killing one hundred tigers.
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 \(P,O,Q\).