Satyagraha: Satyagraha is a philosophy of non-violent resistance that was developed by Mahatma Gandhi. It is based on the principles of truth, love, and self-suffering. It was the primary philosophy that guided his political and social movements.
Swaraj: Swaraj means “self-rule" or “independence" and was an important political objective, but it does not represent the philosophy of non-violence.
Sarvodaya: Sarvodaya is a philosophy that means “welfare of all”, and it talks about an ideal society but is not directly associated with non-violence.
Boycott: Boycott is a method of protest in which one refuses to participate or deal with a particular entity or product, which Gandhi used, but it is not a philosophy of non violence.
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 \(P,O,Q\).