: In 'Adventure' Jayant Narlikar expressed that many world exist simultaneously though they appear to be separated by time. He expressed that the other world also existed and prospered with the world we are aware of. On the other hand, In the third level, Charley a young new York commuter wandering Grand Central Station by accident finds a gateway that leads to a real past of 1894Seizing the opportunity Charley attempts to escape the rat race by buying a one way ticket to his childhood town of Galesburg. Not having proper currency for that period, he forced to postpone his plan to escape to the past.
Why does Charley say, “He (Sam) certainly can’t go back to his old business”? (The Third Level)
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 \(P,O,Q\).