‘Psaltery’ is an ancient musical instrument played by plucking strings. The poet uses the simile of ‘Psalteries of summer’ to describe the natural sounds that the poet hears on a bright sunny day. The natural sounds of the wind playing through the leaves, the chirping of birds, the rapid beating of wings by bees and gnats make the poet feel happy and he does not feel tired listening to the music of nature.
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 \(P,O,Q\).