Dear Students of Class IX,
The Trips and Treks Department is excited to announce a week-long educational trip to Rajasthan during the autumn holidays, offering a chance to explore the rich culture, history, and heritage of this vibrant state.
Trip Details:
Dates: October 20, 2025 - October 26, 2025
Destinations: Jaipur, Jodhpur, and Udaipur
Cost: INR 15,000 per student (includes travel, accommodation, meals, and entry fees)
Registration and Payment:
Interested students must submit the consent form and full payment to the Trips and Treks Department by September 20, 2025. Forms are available at the school office.
Contact Information:
For queries, contact Mr. Rajesh Kumar, Head of Trips and Treks Department, at trips.treks@school.org or call 987-654-3210.
Join us for an unforgettable journey through the land of forts and palaces!
Sincerely,
Mr. Rajesh Kumar
Head of Trips and Treks Department
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 \(P,O,Q\).