Colin Mackenzie's Background: Colin Mackenzie was an engineer, antiquarian and an employee of the East India Company, and his work was crucial in bringing the ruins to light.
First Survey Map: He prepared the first ever survey map of the site of Hampi, which allowed further work at the site.
Information from Priests: He received much valuable information about the location from the memories of priests at the Virupaksha temple and the shrine of Pampadevi, who were very important locals.
Collection of Inscriptions and Pictures: He collected several dozen inscriptions, pictures and studied them which formed a part of his research at the site.
Information from other Sources: He got information from foreign travelers, which further supported his research.
Local History and Surveying Historic Sites: Mackenzie embarked on collecting local histories and surveying historic sites, to better understand India's past, and make governance of the colony easier. He had a clear purpose of his research.
Other Relevant Point: Any other relevant point from the chapter.
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 \(P,O,Q\).