The image of the lady in the story will have different opinions from different readers. The readers can speculate the image of a lady with varying conclusions without a proper description. The author successfully created the lady's appearance as a traditional fortune teller who wore a golden ring shaped like a serpent with emerald eyes. The narration gains a mysterious effect as the story moves on. Readers are still wondering about the lady and her magical ring, which might help the lady dream and interpret her dreams, even at the end of the story. This way, the author succeeds in telling the story effectively to gain the reader's interest.
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 \(P,O,Q\).