The HIV life cycle can be summarized as follows:
Entry and Integration: The virus enters the host body and attaches to CD4 receptors on helper T-cells. It injects its RNA and viral enzymes into the host cell.
Reverse Transcription: Viral RNA is converted into DNA by reverse transcriptase.
Integration: The viral DNA integrates into the host genome with the help of integrase enzyme.
Replication and Assembly: The host cell machinery is used to produce viral RNA and proteins. New viruses are assembled.
Release and Maturation: Newly formed viruses bud off from the host cell, ready to infect other cells. Over time, the number of helper T-cells decreases, leading to immune system failure (AIDS).
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 \(P,O,Q\).