The Australian Downs, a vast region of grasslands, is well-known for Extensive Commercial Grain Cultivation. The region’s large flat plains and suitable climate allow for the large-scale cultivation of grains such as wheat and barley. This form of farming covers large areas with mechanized operations and minimal labor.
Other types of agriculture like Mixed Farming, Plantation Agriculture, and Co-operative Farming are practiced in different regions and do not predominantly represent the Australian Downs.
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 \(P,O,Q\).