Art and literature have played an essential role in preserving the memory of the Revolt of 1857, often referred to as India’s First War of Independence. These mediums have contributed to shaping public consciousness and fostering a spirit of nationalism:
Thus, art and literature not only documented the events of 1857 but also reinterpreted them to instill a sense of pride, resistance, and identity in the Indian populace.
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 \(P,O,Q\).