Here are the journal entries in the books of Ajanta Ltd:
| Date | Particulars | L.F. | Debit (₹) | Credit (₹) |
|---|---|---|---|---|
| 1. | Machinery A/c | 36,00,000 | ||
| To Sujata Ltd. | 36,00,000 | |||
| (Purchased machinery from Sujata Ltd.) | ||||
| 2. | Sujata Ltd. | 36,00,000 | ||
| To Bank A/c | 18,00,000 | |||
| To 8% Debentures A/c | 16,20,000 | |||
| To Discount on issue of debentures | 1,80,000 | |||
| (Payment to Sujata Ltd. Half by bank, balance by issuing debentures at 10% discount) | ||||
In the second journal entry, ₹16,20,000 the amount paid has been calculated as
20,000 * 81 = 16,20,000
The Discount will be = 20,000 * 9 = 180,000
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 \(P,O,Q\).