SUNBEAM PUBLIC SCHOOL, LUCKNOW
CORDIALLY INVITES YOU
The Principal, staff, and students of Sunbeam Public School, Lucknow, cordially invite you to the Annual Awards Function to be held on Saturday, 9th April 2025 at 5:00 p.m. in the school auditorium.
Highlight: Felicitation of National Topper and Live Cultural Performances.
Principal
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 \(P,O,Q\).