Urbanization in India, according to the 2011 census, is unevenly distributed across the states.
States like Maharashtra, Tamil Nadu, and Gujarat exhibit high levels of urbanization due to their industrial growth, economic development, and better infrastructure. On the other hand, states in the northern and eastern parts of India, like Bihar and Uttar Pradesh, have lower levels of urbanization due to various socio-economic factors.
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 \(P,O,Q\).