The beauty and mystery of the Swans’ lives are that as years pass by, their youthfulness remains the same. The poet has grown old, but the Swans have not aged. They carry the same energy and are full of life, even after years have passed; this makes the poet sad. There seems no change in how the Swans carefreely move around or share the love with each other and are connected in brotherhood. The poet gets disturbed as his body refuses to feel energetic again as it once used to be. The mystery is that humans cannot understand the depth of love and family relationships, but the poet believes these swans know the real meaning of life. Hence, the poet feels life is mysterious.
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 \(P,O,Q\).