Malnutrition is a condition that results from an unbalanced diet in which certain nutrients are lacking, in excess, or in the wrong proportions. It includes both undernutrition (wasting, stunting, underweight) and overnutrition (obesity, micronutrient excess). Malnutrition and infection have a bidirectional relationship. Malnutrition weakens the immune system, making a person more vulnerable to infections. Infections, in turn, aggravate malnutrition by decreasing appetite, increasing nutrient requirements, and causing nutrient loss. 
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 \(P,O,Q\).