Sophie and Jansie were different from each other. Sophie was a dreamer who enjoyed creating her own fantasy world using her imagination. She showed an urge to transcend her working-class status and attain sophistication by pursuing the ambition of a fashion designer or an actress. Jansie, on the other hand, was more practical and realistic than Sophie. She tried to pull Sophie back to reality, but all in vain. Jansie’s sensibility and maturity are evident in her attempt to remind her friend that they were earmarked for the biscuit factory, and expensive dreams were inappropriate for their financial status.
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 \(P,O,Q\).