Bessie's justifications for boosting old Hagberd's irrational hopes are as follows:
1) First, she advised Harry to persuade old Hagberd that he is merely his son and return him to his normal state.
2) Second, Harry Hagberd stated, "He isn't frisky—is he?" I'd be terrified of grabbing him. Then she told Harry, to support old Hagberd's foolish hope, "Old Hagberd was the most harmless creature that ever lived."
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 \(P,O,Q\).