“The old one and the young one will be strolling arm in arm to get shaved in my place presently,” the barber laughed as Captain Hagberd walked out of the tap-room of the New Inn near the harbour. He stated that this eccentric old Hagberd, a retired coasting-skipper, was waiting for the return of one of his sons when he noticed a stranger listening to him with a vacuous grin. Barber claims that Colebrook is the only site in the United Kingdom where his longlost sons could be found. Captain Hagberd arrived in Colebrook three years ago after selling his old home in Colchester.
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 \(P,O,Q\).