Radhika Sharma
42 Joy Street
Calpur
26 June 2025
The Head
HR Department
Infotech Services
76 Park Lane
Calpur
Subject: Application for the post of Data Analyst
Dear Sir/Madam,
I wish to apply for the post of Data Analyst. I have a degree in Statistics and over five years of experience in data analysis. I possess strong technical and soft skills, including communication, problem-solving, and programming proficiency. Please find my bio-data enclosed. I look forward to an opportunity.
Sincerely,
Radhika Sharma
Bio-Data:
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 \(P,O,Q\).