Study the following graph carefully and answer the questions that follow :

| Aspect | Stage I (High Fluctuating) | Stage III (Low Fluctuating) |
|---|---|---|
| Characteristics | High birth rates and high death rates, resulting in low population growth. | Low birth rates and low death rates, resulting in very low population growth or decline. |
| Causes | Poor healthcare, high infant mortality, limited food/resources, frequent epidemics. | Advanced healthcare, contraception use, higher education, economic development. |
| Examples | Rainforest tribes, remote communities. | Developed countries like Canada, Japan, USA. |
| Birth Rate | High | Low |
| Death Rate | High | Low |
| Population Growth | Low | Very low or stable |
| Socio-economic Conditions | Primitive or underdeveloped | Highly developed |
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 \(P,O,Q\).