The poet says that virtues like peace, mercy, love and pity are embodied in human beings themselves. Through the above lines, the poet tries to convey how important the virtues are in human life, which would make human life meaningful on earth. Mercy is inside the heart; a human face reflects pity, divine love, and peace permeates the human body with dresses that make humans look beautiful and cultured. With all these virtues in humans, it makes the world look colourful, making life on the earth more beneficial to humans.
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 \(P,O,Q\).