Read the following source carefully and answer the questions that follow:
Amir Khusrau and the Qaul Amir Khusrau (1253–1325), the great poet, musician and disciple of Shaikh Nizamuddin Auliya, gave a unique form to the Chishti ‘sama’ by introducing the qual (Arabic word meaning “saying”), a hymn sung at the opening or closing of qawwali. This was followed by sufi poetry in Persian, Hindavi or Urdu, and sometimes using words from all of these languages. Qawwals (those who sing these songs) at the shrine of Shaikh Nizamuddin Auliya always start their recital with the qual. Today qawwali is performed in shrines all over the subcontinent.
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 \(P,O,Q\).