The study of this region of Antarctica gives us insight into the world’s geological history. It gives an idea, how the earth was like, before it drifted into continents and countries. It shows how slight changes in the climate can change the shape of the region. It gives the explanation how the climatic conditions of the earth were not favourable for life before and how slowly rising temperature made earth a place to sustain life. All secrets are embedded in the layers of ice in the form of half million year old carbon records
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 \(P,O,Q\).