We can certainly say that the older man was very consistent with his madness. There are so many incidents in the story that clearly show that he was somehow mad. When the two went to the barber, he was watching the stance boy there and noticing him. He never shaves his beard; when his wife died, he was a very big smoker, and he thought it would help heal. These points prove the consistency of the older man.
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 \(P,O,Q\).