In the poem, the poet highlights the concept of love which lasts an eternity for most couples. Therefore, the poet has attempted to explain the fragrance of love by defining shadows to compare the bond between two souls who are in love. When it comes to shadows, their length depends on time and the Sun's position during the day. The same philosophy applies to the relationship of love between two people, which reflects the complex factors and circumstances such as emotional outbursts, misunderstandings, etc.
| 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 \(P,O,Q\).