Captain Hagbard prepared all the things his son would love; there was a box full of packets of various flower seeds to choose from for the front garden. They decide to change the full furniture of the cottage so that his son loves it and stays with them forever. He decided to cover the overgrown grass with concrete. These all are the plans Captain Hagberd was preparing for “Tomorrow” when his son was coming.
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 \(P,O,Q\).