
What taluqdars thought
The attitude of the taluqdars was best expressed by Hanwant Singh, the Raja of Kalakankar, near Rae Bareli. During the mutiny, Hanwant Singh had given shelter to a British officer, and conveyed him to safety. While taking leave of the officer, Hanwant Singh told him:
Sahib, your countrymen came into this country and drove out our King. You sent your officers round the districts to examine the titles to the estates. At one blow you took from me lands which from time immemorial had been in my family. I submitted. Suddenly misfortune fell upon you. The people of the land rose against you. You came to me whom you had despoiled. I have saved you. But now – now I march at the head of my retainers to Lucknow to try and drive you from the country.
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 \(P,O,Q\).