The poet uses the imagery of psaltery to outline the summer’s day more picturesquely than a painter could. Furthermore, the poet uses various phrases to explain the scenic beauty of the sun hiding between the clouds, the insects humming, the wind playing through the leaves, and the birds chirping. All these instances in the poem highlight that it is a perfect musical beauty on a summer day. In this unique way, the poet tries to represent the various elements and portrays them more beautifully than any painter.
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 \(P,O,Q\).