Net Factor Income from Abroad (NFIA) is the difference between the total income earned by the residents of a country from abroad and the income earned by foreign residents within the country. It represents the net income generated through cross-border investment and labor.
Components of NFIA:
• Income Earned by Residents Abroad: This includes income from foreign investments, wages earned by citizens working in foreign countries, and any other income generated by the country’s residents from abroad.
• Income Paid to Foreign Residents: This is the income earned by foreign nationals working in the country, along with the income earned by foreign investors in the country.
NFIA = Income earned by residents abroad - Income paid to foreign residents.
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 \(P,O,Q\).