ABC PUBLIC SCHOOL, NEW DELHI
NOTICE
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Date: 25 June 2025
Interhouse Athletic Meet
Our school is organising the Annual Interhouse Athletic Meet on 30 June 2025, from 8:00 a.m. to 1:00 p.m. at the school playground. Events include races, long jump, and discus throw. Interested students (Classes VI–XII) may register by 28 June with the undersigned.
Rishabh Mehta
President, Sports Club
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 \(P,O,Q\).