Sophie’s father has a plumpy face looking grim and sweaty. He doesn't seem to be a soft or sophisticated man. Sophie fears his aggressive manliness. He is a realist and does not believe in his daughter's wild stories. He loves watching football. He hopes young Casey will be as good as Tom Finney. He wishes that the young footballer keeps away from all distractions. He shouts instructions to Casey at the playground. When the Irish genius , beats the hesitant goal keeper, Sophie's father screams with joy and pride. He goes to a pub to celebrate the victory.
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 \(P,O,Q\).