Read the passage given below and answer the questions that follow:
India adopted a democratic approach to the question of diversity. Democracy allows the political expressions of regional aspirations and does not look upon them as anti-national. Besides, democratic politics allows parties and groups to address the people on the basis of their regional identity, aspiration, and specific regional problems. Thus, in the course of democratic politics, regional aspirations get strengthened. At the same time, democratic politics also means that regional issues and problems will receive adequate attention and accommodation in the policy-making process.
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 \(P,O,Q\).