Ancient Indian coinage evolved over several centuries, and its features offer important insights into the economic, political, and cultural life of ancient India. Here are three key features:
1. Metal used: Coins in ancient India were made from a variety of metals, including gold, silver, copper, and bronze. Gold coins were typically issued by kings to signify prosperity and power.
2. Symbolism and Iconography: Coins often carried symbols like animals, deities, or the king's image. For example, the Mauryan coins often featured the wheel (Ashoka Chakra) or elephants, reflecting both religious and political symbolism.
3. Inscription: Many coins, especially during the Mauryan period, featured inscriptions in Prakrit or Brahmi script. These inscriptions often included the names of rulers and their titles, affirming their authority and legitimacy. For instance, the coins issued by Chandragupta Maurya often had inscriptions of his name.
These features reflect the technological advancement and the importance of coinage in administration and trade.
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 \(P,O,Q\).