Nishi had gone to a grocery store to make routine purchases. On reaching home, as she took out Binx tomato chips packet from the bag to give it to her son, she felt that it was underweight. She checked its weight on the kitchen weighing scale and found that it weighed 60 grams whereas the label on the chips packet mentioned the weight of the packet as 100 grams. She approached the manufacturer and complained about it. The manufacturer offered her a gift hamper and requested her not to disclose this to anyone. Nishi refused to accept the gift hamper and took the issue to a redressal agency.

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 \(P,O,Q\).