In this poem, the shadows before and after noon are used to represent the relationship between two people. Noon, which is a brief period, represents the stage of absolute love. Similarly, the shadows before noon are compared to lovers before they completely understand each other. On the other hand, the shadows after noon are meant to describe the maturity of their relationship. Hence, the shadow before Noon is apparent, whereas, in the afternoon, it fades away.
| houres shadowes Sunne noone clearnesse behinde |
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 \(P,O,Q\).