The act of nature in the poem is expressed as precise or accurate because nature tries to neutralise every condition with precision after every specific interval of time. Thus, in verse, the poet specifies time honouring someone's desire at a time. Moreover, the poem talks about the long-lasting quarrels between the Hindu, Muslims, and Christians that have been resolved over time by nature. Hence nature echoes the title of the poem "Time and Time Again".
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 \(P,O,Q\).