Eveline, in the story, was in a confused state of mind to choose between responsibility and happiness. To keep the promise, she had given to her mother, she had to look after the family, stay together, and not let family relationships break. For this, she had to sacrifice her precious life. Even though she had an opportunity to start a happy and peaceful life with her beloved Frank, all the promises, memories and relationships flashed in front of her eyes, making her give up her dreams and embrace the well-being of her family. Often, there is always a conflict in one's life when a person has to choose between their personal life, family, happiness, and future. Eveline also went through the same situation, making it difficult to choose between her abused life with her family or escaping with her beloved one. Thus, in society, choosing happiness becomes problematic and selfish, pulling back a person to fulfil their filial duty, sacrificing their personal life
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 \(P,O,Q\).