KOHINOOR PUBLIC SCHOOL, HAWAPURI
NOTICE
INTER-HOUSE BOOK REVIEW COMPETITION
All students of Classes IX–XII are hereby informed that an Inter-House Book Review Competition will be organised on 30th June 2025 in the School Library from 11:00 a.m. onwards. Each house may nominate 2 participants. Interested students must register with the undersigned by 27th June.
Aruna / Arun
(Head Girl / Head Boy)
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 \(P,O,Q\).