Milton describes Shakespeare as the source of inspiration for all succeeding generations of poets by saying that his statements leave an enduring impression in his readers' minds. Meanwhile, one reads or listens to his sonnet or play, and they are left astonished and become fascinated and paralyzed with wonder. So, they are stunned to become marble statues in the tomb of Shakespeare over succeeding time. These works even astonish future generations, passed on from the previous one.
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 \(P,O,Q\).