• She had consented to go away, to leave her home. • Strange that it should come that very night to remind her of the promise to her mother, her promise to keep the home together as long as she could. • She prayed to God to direct her, to show her what was her duty. • Frank would take her in his arms, fold her in his arms. • Her time was running out but she continued to sit by the window, leaning her head against the window curtain, inhaling the odour of dusty cretonne. • Not long before, when she had been laid up for a day, he had read her out a ghost story and made toast for her at the fire.
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 \(P,O,Q\).