Sophie was a dreamer who often made up stories for herself and for others. One possibility might be that she wanted to escape the squalor of daily life with the help of her fantasies. Her encounter with Danny Casey was a made-up story for the sake of catching her brother's attention. Eventually, she got so much engrossed in it that she started to live in the world of fantasy. When Danny Casey did not arrive for the second 'date', she experienced disappointment. However painful and disappointing her fantasy might be, she was not willing to accept reality. Her dreams and disappointments are figments of her imagination.
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 \(P,O,Q\).