The 'trees in their autumn beauty', 'dry woodland paths', 'October twilight', and 'still sky' all indicate the poet's loneliness and old age. Autumn is the season where trees decay and shed their leaves. The woodland remains dry and barren, and there would be no new life evolving until it rains. Though the twilight is the most beautiful part of the day, it lasts for a brief period and traverses into the long darkness of night. The stillness of the sky is when there is no movement in the body, comparing it to the coldness of death. So, the poet's imagination is closely associated with the poet's old age and the setting in sadness and loneliness.
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 \(P,O,Q\).