The Harappan civilization, one of the earliest urban cultures, showcased advanced urban planning:
1. Grid Pattern Town Planning: Cities like Mohenjo-Daro and Harappa were built on a grid layout, with streets intersecting at right angles.
2. Drainage System: A sophisticated underground drainage system ensured sanitation and hygiene.
3. Public and Private Architecture: Cities had public structures like the Great Bath and granaries alongside private dwellings with standardized bricks.
4. Trade and Commerce: Harappan cities were centers of trade, with evidence of interactions with Mesopotamia and Central Asia.
5. Standardized Weights and Measures: Uniform systems of weights and measures indicate organized economic activities.
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 \(P,O,Q\).