Sophie belongs to a lower middle class. She lives in a small house with her parents and two brothers, Derek and Geoff. When she returns home after school, she feels choked with the steam of the stove and is disgusted with the dirty dishes piled in a corner. Her mother's back has become stooped and bent by handling all the household chores and responsibilities on her own. Her father is a hard labourer and her elder brother, Geoff works as an apprentice mechanic in a garage situated far away from his house. Her family wants Sophie to join work immediately after her school. These are some of the indicators of the financial status of Sophie's family.
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 \(P,O,Q\).