Questioning or inquiring about the current set of laws and regulations imposed upon us will help develop other aspects and lead to the development of our intellectual society. The inquiry process leads to absolute freedom, which makes us think deeply and discover what is true and false. Hence, we would grow stronger mentally and gain more knowledge than we could have received when rules bound us. So, the author tries to tell us that instead of blindly following the rules, we must inquire about the traditional significance to have a more comprehensive understanding of their importance. Thus, we can secure several perspectives and develop our minds, leading us to true freedom.
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 \(P,O,Q\).