Jilani Jung Jung Bahadur, the king of Pratibandapuram, is known as the Tiger King. At the time of his birth the astrologers declared that the prince would have to die one day. The ten-day-old prince asked the astrologers to reveal the manner of his death. The wise men were baffled at this miracle. The chief astrologer said that the cause of his death would be a tiger. The young prince growled and uttered terrifying words: 'Let tigers beware!' He decided to kill one hundred tigers. He thus got the name 'Tiger King'.
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 \(P,O,Q\).