During secondary treatment of sewage, the BOD of the effluent is reduced through the following processes:
- Consumption of organic matter: Aerobic microorganisms in the effluent consume the organic matter.
- Formation of flocs: Microbial activity leads to the formation of flocs, which are aggregations of bacteria and fungi.
- Decomposition of organic matter: Organic matter is broken down into simpler substances like carbon dioxide and water.
- Separation of activated sludge: The flocs settle down as activated sludge, further reducing the organic load.
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 \(P,O,Q\).