Teenage is the phase of life which constitutes the major changes in the life of an individual. During this phase, a person learns many things, sets his career goals, and deals with peer pressure and the pressure of adult's expectations. Hence, it is natural for teenagers to fantasize and to have unrealistic dreams.
Advantages: Fantasizing, based on realistic goals or the world around, provides a means to reach higher ambitions and dreams. Aspiring for higher career goals and working hard may ensure successful career prospects. Thus it instills confidence and a spirit to achieve one's desire. In difficult situations of life it helps instill positivity and optimism. Those who do so can be judged as creative people.
Disadvantages: Fantasizing builds a gap between fantasy and reality. The realization of the disparity between one's goals and capabilities may be painful. Non achievement may also lead to disappointment, depression or suicidal tendencies. Moreover, it is a sheer wastage of time for many.
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 \(P,O,Q\).