The 'light tread' refers to how the poet would walk freely some nineteen autumns ago. Then, he was a free man with no worries and would go around for days wherever he wished to, the same way the Swans did. But now, he has a 'sore heart', which indicates a slight pain in the heart. At the same time, when looking at the Swans moving around freely and carefree reminds him of the responsibilities he has been tied to, and he has a lot to worry about. He feels he can no longer walk around like a free soul. Neither do his physical or mental conditions allow him to do so.
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 \(P,O,Q\).