Lost and Found Department
This is to inform all students that the school has set up a 'Lost and Found Department' in the main office. Any student who has lost an item is requested to report the following details:
- A brief description of the lost item
- The date, time, and location where it was lost
- Contact information
Please report all lost items promptly to help us return them to their rightful owners.
For more information, visit the Lost and Found Department.
President, Lost and Found Department
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 \(P,O,Q\).