(a.) You are a student counsellor of N.J. Public School. You are invited by S.M. International School, Kala Puram, to address Class XII students on Goal Setting & Time Management. Write a formal letter of reply accepting the invitation and confirming your presence at the stated time, including relevant details.
(a) Formal Letter of Acceptance
N.J. Public School
15th January 2025
The Principal
S.M. International School
Kala Puram
Subject: Acceptance of Invitation to Address Class XII Students
Dear Sir/Madam,
I am pleased to accept your invitation to address the Class XII students of your esteemed institution on the topic of "Goal Setting & Time Management." I confirm my presence at the scheduled time, 10:00 AM, on 20th January 2025. I look forward to interacting with the students and contributing to their growth and learning.
Thank you for the opportunity.
Warm regards,
[Your Name]
Student Counsellor
N.J. Public School
Letter Writing: A1 or A2. Do any one of the following: Situation:
Uncontrolled use of mobile phones and video games is affecting school-going children. As a result, they are suffering from many diseases. Imagine you are Saurabh/Shrushti, residing at Malad, Mumbai. You read the above clipping in the newspaper. Write a letter to the editor expressing your concern about this issue.
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 \(P,O,Q\).