In today's world, the Industrial Revolution, the age of machinery, new technologies have developed rapidly with the production of goods that have opened doors for humankind. There have been new-age technologies that have helped speed up agricultural domains and result in overgrowing productions. 'Nature may have tricks up her sleeve to check us if the chemists exploit her too greedily' is related to today's context as overexploitation of resources is very harmful to today's Nature. When all these technologies override Nature without any control, we humans have to face many problems in the future. The use of chemical fertilisers in factories, agricultural fields create a varied impact on Nature. Thus, the author, G.B Shaw, means that there should be a check on natural resources.
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 \(P,O,Q\).