The author thought that Frau Frieda's dreams were a stratagem for surviving because she had revealed about herself that she sold her dreams by foretelling fate about others in the town and had made more fortune out of it. Then she was hired at a salary that covered her minor expenses to predict a religious family's fate at Viennese. So, the author had always thought her dreams were no more than a stratagem for surviving, which never surprised him.
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 \(P,O,Q\).