The Reserve Bank of India (RBI) performs the following functions as the ‘Banker’s Bank and Supervisor’:
Banker’s Bank: The RBI acts as a banker to all scheduled commercial banks. It provides short-term funds, acts as a lender of last resort, and facilitates inter-bank clearing.
Supervisor: The RBI supervises and regulates banks to ensure financial stability. It monitors compliance with banking regulations, manages non-performing assets (NPAs), and ensures that banks maintain required reserves. These functions help in maintaining stability and liquidity in the financial system.
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 \(P,O,Q\).