Alexander Cunningham:- was a British engineer and archaeologist who was appointed as the first Director-General of the Archaeological Survey of India (ASI) in 1871. His work laid the foundation for systematic archaeological research in India. He is known for his extensive surveys, documentation, and excavations of numerous sites, and is considered the Father of Indian Archaeology.
John Marshall:- was a later Director-General of the ASI, and is known for overseeing the excavations of Harappa and Mohenjo-Daro in the 1920s which led to the discovery of the Indus Valley Civilization. His contribution was also invaluable, but he was not the first director general.
Daya Ram Sahni:- was an Indian archaeologist known for his work in the Indus Valley Civilization and particularly for the excavation of Mohenjo-Daro. He worked under John Marshall, and was not a director general.
S.N. Roy:- was a scholar and historian, and his contribution was primarily to history and not archaeology. He did not hold any post at ASI.
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 \(P,O,Q\).