Many families in our country are unable to meet even the basic needs of their members and/or access as well as utilise the various services provided by other structures of the society due to various reasons, one of them being lack of resources, especially financial. Further, many children, youth and elderly are separated from their families and are left to cope on their own. By themselves, they find it difficult to meet their own needs.
| List-I (Initiative) | List-II (Year) |
|---|---|
| i. SOS Children’s Villages | 4. 1964 |
| ii. National Youth Policy | 1. 2000, 2015 |
| iii. National Policy for Older Persons | 2. 1999 |
| iv. Juvenile Justice (Care and Protection of Children) Act | 3. 2003, 2014 |
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 \(P,O,Q\).