Following is the extract of the Balance Sheet of Sankalp Ltd. as per Schedule III, Part I of the Companies Act, 2013 as at 31st March, 2024 along with the notes to accounts: Balance Sheet of Sankalp Ltd. as at 31st March, 2024 (An extract)}
| Particulars | 31.03.2024 (₹) | 31.03.2023 (₹) |
|---|---|---|
| I – Equity and Liabilities | ||
| 1. Shareholders’ Funds | ||
| (a) Share Capital | 29,80,000 | 25,00,000 |
Notes to Accounts as at 31 st March, 2023
| Particulars | 31.03.2023 (₹) |
|---|---|
| Authorised Capital 4,50,000 Equity Shares of ₹10 each | 45,00,000 |
| Issued Capital 2,50,000 Equity Shares of ₹10 each | 25,00,000 |
| Subscribed Capital Subscribed and fully paid-up 2,50,000 Equity Shares of ₹10 each | 25,00,000 |
| Subscribed but not fully paid-up | NIL |
| Total | 25,00,000 |
Notes to Accounts as at 31st March, 2024
| Particulars | 31.03.2024 (₹) |
|---|---|
| Authorised Capital 4,50,000 Equity Shares of ₹10 each | 45,00,000 |
| Issued Capital 3,00,000 Equity Shares of ₹10 each | 30,00,000 |
| Subscribed Capital Subscribed and fully paid-up 2,90,000 Equity Shares of ₹10 each | 29,00,000 |
| Subscribed but not fully paid-up 10,000 Equity Shares of ₹10 each fully called-up | 1,00,000 |
| Less: Calls-in-Arrears 10,000 Equity Shares @ ₹2 per share | 20,000 |
| Total | 29,80,000 |
Answer the following questions:
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 \(P,O,Q\).