Nature of Business: The type of business a company operates has a significant impact on its fixed capital needs. For example, a manufacturing company requiring heavy machinery, a production plant, and specialized equipment will have substantially higher fixed capital needs compared to a service-oriented business like a consulting firm or a small retail shop, which may only require office space, furniture, and computers.
Scale of Operations: Companies operating on a larger scale generally need more fixed capital than those with smaller operations. Expanding production capacity, acquiring more land and buildings, and investing in automated equipment all increase the need for fixed capital. Conversely, a smaller scale of operations allows a company to manage with a lower investment in fixed assets.
Technology Upgradation: Industries that experience rapid technological advancements often require significant investments in new machinery, equipment, and infrastructure. Companies in these sectors need to allocate substantial fixed capital to keep up with the latest technology, improve efficiency, and maintain a competitive edge. However, some companies choose leasing as an alternative to purchase such equipment to avoid large upfront expenses.
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 \(P,O,Q\).