His life was a whirlwind as he told Bessel, "I've done virtually anything you can conceive of save a tailor or a soldier." I've sheared sheep, humped my swag, and harpooned a whale as a boundary rider. I've rigged ships, prospected for gold, skinned dead bullocks, and passed up more money than the old guy would have scraped together in his lifetime.
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 \(P,O,Q\).