Read the given source carefully and answer the questions that follow:
Harappan Settlements
So far, more than 2000 Harappan archaeological sites have been discovered in the Indian sub-continent. Most of the sites are found located between the Indus and the Saraswati River basins. Nearly two-thirds of these settlements are in the Saraswati basin, suggesting its immense importance for the Harappan Civilisation. Among these, five major cities have been identified. These are Rakhigarhi, Mohenjodaro, Harappa, Dholavira and Ganweriwala. The remaining sites come under different categories such as Regional Centres, agricultural villages, ports and manufacturing centres.
Examine the role of rivers in sustaining the Harappan settlements.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 \(P,O,Q\).