Read the following source carefully and answer the questions that follow:
The orders of the king
Thus speaks king Devanampiya Piyadassi: In the past, there were no arrangements for disposing affairs, nor for receiving regular reports. But I have made the following (arrangement). Pativedakas should report to me about the affairs of the people at all times, anywhere, whether I am eating, in the inner apartment, in the bedroom, in the cow pen, being carried (possibly in a palanquin), or in the garden. And I will dispose of the affairs of the people everywhere.
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 \(P,O,Q\).