Dreams and clairvoyance are an element of the poetic vision as religious superstition. Dreams are the base work on any excellent poem, including assumptions and formulating events according to ourselves. Most of the poet's dreams are the root to create a poem, and clairvoyance enriches the readers with the poet's creativity and dreams. Clairvoyance is also part of religious superstitions as priests. Many fortune-telling priests tell their superstition stories to the people by making them believe that they dreamt about it and easily make them believe that they know their fate.
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 \(P,O,Q\).