ABC HIGH SCHOOL
123 Education Lane, Knowledge City
July 5, 2025
NOTICE: EXTRA CURRICULAR CLUBS REGISTRATION
Dear Students,
We are pleased to inform you that our school is launching various extracurricular clubs to help you explore your interests and develop new skills. These clubs will operate every Wednesday from 2:00 PM to 3:30 PM beginning August 5, 2025.
The following clubs will be available:
Registration Details:
To register, please visit the school office or register online at www.abcschool.edu/clubs.
For more information, contact the organizing committee at clubs@abcschool.edu or visit room 205 during lunch break.
We encourage all students to participate and make the most of these opportunities!
Sincerely,
John Smith
Head, Organizing Committee
ABC High School
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 \(P,O,Q\).