The future of the humankind can get in danger if the emission of carbon- dioxide and other poisonous gases go on in the same manner. These gases deplete the ozone layer and allow the ultra-violet rays of the sun to enter the earth’s environment. This causes the rise in temperature of the earth and giving rise to the phenomenon called global warming. Increased temperature can melt the ice of the Antarctica, and cause other environmental problems, thus jeopardizing the future of human kind.
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 \(P,O,Q\).