XYZ HIGH SCHOOL
HEALTH CLUB
July 5, 2025
INTERACTIVE SESSION ON HEALTH AND SAFETY GUIDELINES
Dear Students of Classes IX-XII,
The Health Club is organizing an interactive session on "Health and Safety Guidelines" to empower students with essential knowledge about maintaining health and safety in school and at home.
Session Details:
Session Highlights:
Registration Information:
To register, please:
For queries, contact Health Club members or email healthclub@xyzschool.edu
Your health is your wealth! Don't miss this valuable learning opportunity.
Sincerely,
Rahul Verma
President, Health Club
XYZ High 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 \(P,O,Q\).