Harry Hagberd, Captain Hagberd's son, was the stranger. Captain was anxious at first meeting a stranger since the other was talking about his kid, and then he lost control when the stranger said, "The devil he is!" Captain began shouting, his feet squelched in the puddles left by his work, as the stranger gazed in awe. He crawled across the destroyed grass plot's holes. He dashed into the barrier, blindly.
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 \(P,O,Q\).