Bhagirath Lane, Uttarbagh
July 5, 2025
Dear Esteemed Guest,
The Management, Staff, and Students of St. Rose School cordially invite you to a Cultural Evening Fundraiser to support the construction of a new wing for our school building, aimed at enhancing educational facilities for our growing student community.
We are delighted to present a compelling highlight of the evening: a mesmerizing performance by the renowned classical dance troupe, NatyaVriksha, showcasing a blend of traditional and contemporary Indian dance forms that promise to captivate and inspire.
Event Details:
Kindly confirm your attendance by August 2, 2025. For reservations or inquiries, please contact our Event Coordinator, Ms. Anita Sharma, at events@stroseschool.org or call +91-987-654-3210.
Your presence and generous support will help us build a brighter future for our students. We look forward to an evening of cultural enrichment and community spirit.
Sincerely,
Rubaya/Roopesh Khan
Principal, St. Rose School
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 \(P,O,Q\).