The astrologer dies before the king of Pratibandapuram gets an opportunity to kill one hundred tigers. Disproving his prophecy seems to be the sole reason for the king's existence. Except for killing hundred tigers, everything else takes a back-seat for the king. The prophecy cannot be indisputably disproved as the king was ultimately killed by a tiger, though neither by a real one nor by the hundredth one. Looking at the weak, old and almost lifeless tiger that was the hundredth one, no one would have thought that it would escape the king’s bullet by fainting at the shock of the bullet whizzing past. It was the “tiny little wooden tiger” from the toy shop that caused the death of the 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 \(P,O,Q\).