The way Charley came across Sam’s letter was surrounded in mystery. Among his oldest first-day covers, he found an envelope. The envelope containing the letter bore the address of his grandfather. It was written on July 18, 1894. The postmark showed the Picture of President Garfield. Generally the first day covers have blank papers in them, but this one contained a letter. The letter was addressed to Charley. In the letter Sam had informed Charley that he was living on the third level. He had also told Charley and his wife to keep looking for the third level. Clearly, the letter was a product of Charley’s imagination.
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 \(P,O,Q\).