Antarctica gives us an idea, how the earth would have been like millions of years ago and how it got divided into various earth masses. The melting and colliding ice masses also give us an insight into how our future is going to be, if we continue with interference in the working of the nature. Moreover, Antarctica holds into the depths of its ice half-million year old carbon records, which are helpful in understanding the past, present and future of the earth. Therefore, Antarctica is the place which reveals our past, shows our present and visualizes our future
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 \(P,O,Q\).