Read the following table & passage and answer Question Nos. 15 to 17:
International Comparison of Human Development
Human Development Categories
| Level of Human Development | Score in Development Index |
| Very High | above 0.800 |
| High | between 0.700 up to 0.799 |
| Medium | between 0.550 up to 0.699 |
| Low | below 0.549 |
The priority of countries with high level of human development is providing education and healthcare. They are investing more in social sector. Altogether, a higher investment in people and good governance has set this group of countries apart from others.
Countries with medium levels of human development have emerged in the period after the Second World War. Many of these countries have been rapidly improving their human development score by adopting more people-oriented policies and reducing social discrimination.
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 \(P,O,Q\).