The geological phenomenon of separating various continents and water bodies from one compact landmass tells us about the age of existence of human race on the earth. Six hundred and fifty million years ago, no human race existed on the earth because the environment was not favorable. After the time when the dinosaurs were wiped out, the Mammals started existing and after the separation of landmass, the human race started flourishing on the earth.
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 \(P,O,Q\).