Parent-Teacher Meeting
This is to inform all students that the upcoming Parent-Teacher Meeting will be held on 15th June 2025 at 10:00 AM in the school auditorium. Parents are requested to attend the meeting to discuss their child's academic progress. Please inform your parents in advance. Attendance is mandatory.
For further details, contact the Activities In-charge.
Date: 10th June 2025
Activities In-charge
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 \(P,O,Q\).