The poet, A.K Ramanujan, describes time, how time affects different cities. The poem discusses different cities and how time is involved in those cities. While beating their gongs around the clock, the clock strikes, and time flies, leading to some changes occurring in the city. As time passes, every single hour of the clock represents the changes in the city. Once the old-time ends, everything starts from the beginning as a new time arrives.
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 \(P,O,Q\).