The family area in landscape and garden design is a designated space meant to serve the daily needs of family members. Its functions include:
| Group I | Group II |
| (P) Edge City | (1) Rapid expansion of geographical areas of towns or cities |
| (Q) Synekism | (2) Violence against the city |
| (R) Urbicide | (3) A secondary CBD on the edge of the city |
| (S) Urban Sprawl | (4) Rebuilding core city area |
| (5) Union of several small urban settlements under one rule |
| Group I | Group II |
| (P) Gulf of Mannar | (1) Ridge, Glacier |
| (Q) Sunderbans | (2) Sub-tropical/Tropical Forest, Stepped Hill |
| (R) Nanda Devi | (3) Swamp forest, Mangrove |
| (S) Nilgiri | (4) Coral Reefs, Seagrass bed |
| (5) Salt Marsh, Flat Terrain |
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 \(P,O,Q\).