‘Send him away, my darling,' Captain Hagberd shouts from the window to Bessie. He's just a wanderer. What you really want is a nice place to call your own. That guy doesn't have a house; he's not like Harry. He can't possibly be Harry. Harry will arrive the next day. Do you hear what I mean? ‘One more day,' he exclaimed, ‘and you will never fear—Harry will marry you.'
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 \(P,O,Q\).