In the poem, the poet talks about the shadows, representing the ups and downs in a relationship based on love. The shadow expresses a bonding between two people, which deepens over time and is tested gradually, blossoming into a beautiful relationship. The length of the shadow portrays maturity in love. As depicted in the poem, the shortest span of the shadow is at noon, expressing complete understanding between two people.
| 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 \(P,O,Q\).