Bio-energy is a renewable source of energy derived from organic materials such as plant and animal matter. In India, bio-energy plays a significant role due to its potential to address multiple challenges, including energy shortages, environmental sustainability, and rural development.
1. Renewable Energy Source: India faces increasing energy demands, especially in rural and remote areas. Bio-energy offers a renewable and sustainable energy source by utilizing agricultural waste, forest residues, and animal manure. This can help reduce reliance on fossil fuels, ensuring long-term energy security.
2. Waste Management: Bio-energy is produced from organic waste, which helps address waste disposal issues, particularly in urban and rural areas. By converting agricultural residues and other waste into energy, it minimizes environmental pollution and encourages recycling.
3. Reduction in Greenhouse Gas Emissions: Bio-energy is considered a cleaner energy source as compared to traditional fossil fuels. It helps reduce greenhouse gas emissions, thus contributing to India's commitment to combating climate change and promoting sustainable development.
4. Economic Growth and Job Creation: The development of bio-energy projects promotes local economic growth, particularly in rural areas. It provides employment opportunities in agriculture, technology development, and energy production, thereby enhancing economic stability in underserved regions.
5. Improved Energy Access: Bio-energy technologies such as biogas and biomass plants can provide clean and affordable energy to rural areas, where conventional electricity supply is often unreliable. This contributes to improving the quality of life by meeting basic energy needs.
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 \(P,O,Q\).