J. Krishnamurti believed that discipline and freedom are contradictory to one another. Disciplines are a set of rules to be followed with certain morals. When bound by such laws and regulations, people cannot achieve their required freedom. No individual can question the rules; hence there cannot be any intellectual development or free-thinking, and thus, can never achieve true freedom. We become self-controlled and cannot be in a stage to help other struggling individuals. Ordinary people do not have any right to question, follow the traditional rules blindly, and there would not be any developmental growth, resulting in loss of freedom. Thus, the concepts of freedom and discipline contradict each other.
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 \(P,O,Q\).