In the story, Gandhi makes it possible for the sharecroppers of Champaran to shed their fear of the British landlords. According to Gandhi, freedom from fear is the first step towards self-reliance. However, it is unfortunate that the poor of the country are not free from fear, even decades after the independence. Their actions, work, etc. are still under pressure; they are at the mercy of the bureaucratic system. Furthermore, the poor live in a continual fear of the police, who instead of taking care, often end up maltreating them. The already poor farmers are becoming poorer, because of globalisation and the craze for the foreign products. This leaves them in the fear of further destitution.
“This settlement was adopted unanimously by the commission. Gandhi explained that the amount of the refund was less important than the fact that the landlords had been obliged to surrender part of the money and, with it, part of their prestige. Therefore, as far as the peasants were concerned, the planters had behaved as lords above the law. Now the peasant saw that he had rights and defenders. He learned courage.”
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 \(P,O,Q\).