Nature always has some amount of control over every living being. As part of Nature itself, human beings cannot escape from Nature's responsibilities upon us. In the first type of slavery, the essential habits of every human, like eating, drinking, sleeping etc., are all a part of Nature's control over us. It is physically impossible to escape these duties as we are all slaves to Nature. However, in the second type of slavery, man to man slavery, the work pressure is given from person to person or any external force. It's our call whether to continue or to avoid that person's instructions. Hence, we can choose whether to follow a leader or unfollow based on the circumstances of our situation in the broader political sphere. However, in the personal sphere, we are all slaves to Nature and cannot choose when complying with its orders. Hence, people are subjected to greater control in their personal sphere than in the wider political sphere.
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 \(P,O,Q\).