J.M. COLONY RESIDENTS WELFARE ASSOCIATION, PAWANSHAHR
NOTICE
FREE EYE CARE CAMP FOR SENIOR CITIZENS
All residents are informed that a Free Eye Care Camp will be organised on 5th July 2025 from 9:00 a.m. to 1:00 p.m. at Community Hall in collaboration with Shanti Hospital. Senior citizens of our colony are requested to avail this opportunity.
Renuka / Rahul Bhatia
(President, RWA)
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 \(P,O,Q\).