Preeti started her own cooking channel on Youtube ‘Mood Art’. As her subscribers increased, she was not in a position to manage everything on her own. She hired Rahul and Riya to help her with filming, editing, lighting and content research. She granted authority to them to operate within prescribed limits. She was thus, able to use her time on high priority activities like developing new recipes and content development etc. As a result, Rahul and Riya were given opportunities to develop and exercise initiative. Preeti was now able to focus on objectives and meet the target of achieving a subscriber base of one million in six months.
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 \(P,O,Q\).