Study the given figure carefully and answer the questions that follow :
| Open-cast Mining | Shaft Mining |
|---|---|
| Used for extracting minerals that lie close to the surface. | Used for extracting minerals that lie deep below the surface. |
| Involves removal of surface layers to reach the mineral deposit. | Involves digging deep vertical shafts to access underground minerals. |
| Less expensive and less dangerous. | More expensive and riskier due to depth and safety concerns. |
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 \(P,O,Q\).