Umberto Eco: Aah, now that is more difficult to explain. I have some philosophical interests and I pursue them through my academic work and my novels. Even my books for children are about non-violence and peace ... you see, the same bunch of ethical, philosophical interests. And then I have a secret. Did you know what will happen if you eliminate the empty spaces from the universe, eliminate the empty spaces in all the atoms? The universe will become as big as my fist. Similarly, we have a lot of empty spaces in our lives. I call them interstices. Say you are coming over to my place. You are in an elevator and while you are coming up, I am waiting for you. This is an interstice, an empty space. I work in empty spaces.
(The Interview)
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 \(P,O,Q\).