The famous writer, J. Krishnamurti, gives us an honest insight into the concepts of freedom and discipline. So, according to him, respecting elders is not to be confused with blind obedience. On the contrary, respecting elders is very much essential. Respecting and obeying elders is the usual tradition of our society. We are usually instructed never to question them, and sometimes to follow the same, which is said to be very helpful to us. However, obedience and blind obedience both have different meanings. Obedience is when individuals will have their ethics in their thoughts and check whether the elders' advice meets our views on the topic, and blind obedience is slavery, not freedom. Hence, one can never achieve true freedom through blind obedience, and it does more harm than good.
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 \(P,O,Q\).