In the poem, the poet addresses his beloved one to convey the different stages of love to her. The poet tries to explain to his lady love that everything seems to be excellent and creamlike when the love is fresh. At the initial stage, people who are deeply in love tend to forget themselves. As they grow older, the relationship also gets more assertive, and they get to know each other much more closely and deeper, gaining a clear understanding of life. Over time, love grows with maturity encouraging them to fight all the odds, and face the ups and downs they come across.
| 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 \(P,O,Q\).