Derry: I’d not come to steal anything. Mr. Lamb: No, no. The young lads steal...scrump the apples. You’re not so young. Derry: I just...wanted to come in. Into the garden. Mr. Lamb: So you did. Here we are, then. Derry: You don’t know who I am. Mr. Lamb: A boy. Thirteen or so. Derry: Fourteen. [Pause] But I’ve got to go now. Good-bye. Mr. Lamb: Nothing to be afraid of. Just a garden. Just me. Derry: But I’m not...I’m not afraid. (Pause) People are afraid of me.
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 \(P,O,Q\).