Geoff Green took the high school students to one end of the world, to provide them the opportunity to develop the respect and understanding for the earth. He wanted to make the future policy-makers to experience how difficult it would have been for the earth to sustain life by rising its temperature. He wanted them to understand that any interference in nature can cause drastic mishappenings in the future when the students see the ice shelves melting and collapsing, they can estimate the kind of environmental troubles ahead in their 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 \(P,O,Q\).