The posterity or future generations have considered Shakespeare's plays and poetry as a great work of English Literature. As a tribute, today's generation has kept his memory alive in their hearts and minds through his works. The works of Shakespeare have driven inspiration for the present generation. People read, learn lessons for life and celebrate from the plays and dramas of Shakespeare. Thus, he is remembered as a 'live long monument' in people's hearts. Shakespeare's death anniversary is celebrated every year in Stratford-upon-Avon to pay tribute to this literary genius.
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 \(P,O,Q\).