The writer was a prose-writer. He wanted to send a short story for the short story contest organized by a British periodical by the name 'The Encounter'.
At last, around four in the afternoon, the poet (or the editor) arrived. He was a tall man, very English, very serious and of course very unknown to all of us. Battling with half a dozen pedestal fans on the shooting stage, The Boss read out a long speech. It was obvious that he too knew precious little about the poet (or the editor). The speech was all in the most general terms but here and there it was peppered with words like 'freedom' and 'democracy'. Then the poet spoke. He couldn't have addressed a more dazed and silent audience — no one knew what he was talking about and his accent defeated any attempt to understand what he was saying.
(Poets and Pancakes)
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 \(P,O,Q\).