The angle of deviation (δ) of light passing through a prism varies with the angle of incidence (i) as shown below. The angle of deviation initially decreases, reaches a minimum value, and then increases as the angle of incidence increases
Definition of Minimum Deviation (δm):
The angle of minimum deviation (δm) is the smallest angle of deviation that occurs when the light passes symmetrically through the prism, i.e., when the angle of incidence equals the angle of emergence.

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 \(P,O,Q\).