Dear Students,
We are thrilled to announce that our school will be hosting an Inter-School Science Symposium to foster innovation and scientific curiosity among students.
Event Details:
Date: Saturday, August 15, 2025
Time: 9:00 AM to 3:00 PM
Venue: School Auditorium, Main Campus
Participation Details:
Students from grades 6 to 12 are invited to participate by presenting projects, posters, or models on any scientific topic. Teams of up to 3 students are allowed. Register your team and submit a brief project abstract (150-200 words) by July 25, 2025.
Submission Guidelines:
Submit your project abstract to the Cultural Committee Office or email it to science.symposium@school.org. Selected teams will be notified by July 30, 2025.
Contact Information:
For queries, contact Ms. Anita Sharma, Head of Cultural Committee, at culturalcommittee@school.org or call 123-456-7890.
Let’s celebrate science and innovation together!
Sincerely,
Ms. Anita Sharma
Head of Cultural Committee
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 \(P,O,Q\).