Sarnath: The first sermon of the Buddha, also known as the “Dhammacakkappavattana Sutta" was delivered at Sarnath, near Varanasi. This was a major event in the history of Buddhism, as it was a formal setting out of his teachings.
Bodh Gaya: Bodh Gaya is where Buddha attained enlightenment, but this was not the place where he delivered the first sermon.
Amravati: Amravati is a significant Buddhist site in Andhra Pradesh, but not related to Buddha's first sermon.
Sanchi: Sanchi is an important Buddhist site known for its stupas and other structures, but is not where Buddha delivered his first sermon.
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 \(P,O,Q\).