Bessie Begin was a woman who notices everything but generally doesn’t share her feelings. She explains the insanity of Hagberd with the stranger by saying that he has lost his son in the sea and the dreams of his son; he always dug in the front yard but never planted anything because he was waiting for his son, but the son was not coming back home and when he got to know that his son is coming “tomorrow” he then decided to plant the flowers.
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 \(P,O,Q\).