‘Shanta Enterprises’ was in the business of manufacturing solar panels for the last fifteen years. With their expertise now they were able to manufacture good quality solar panels at lower cost. As a result ‘Shanta Enterprises’ was flooded with orders and was able to generate a good profit margin.
To motivate the employees the company decided to compensate some of them for their hard work. Arvind and Yogesh, who were working on contract basis, were absorbed permanently in the company. Both were happy as now there was stability about their future income. Ekta, a regular employee of the company, working as Research and Development Head, was awarded the ‘Best Employee of the year Award’.
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 \(P,O,Q\).