According to Bergman, one cannot put a novel into a film entirely. It becomes a complete injustice to the book because it triggers the intellectual faculty, whereas the movie triggers emotions directly.
However, according to Umberto Eco, the film takes over the popularity of a novel. It is only when the movie is made out of a book that it reaches the epitome of its popularity. So, the film indirectly helps the novel. Thus, Bergan believes that the individual effect of each of these two art forms on the audience is different from each other.
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 \(P,O,Q\).