The sexual reproduction phase of Plasmodium occurs in mosquitoes, making them the definitive hosts of the parasite.
Gametocytes: Male and female gametocytes are ingested by a mosquito during a blood meal.
Fertilization: Gametocytes fuse in the mosquito's gut to form a zygote.
Development: The zygote develops into an ookinete, which penetrates the gut wall and forms an oocyst.
Sporozoites: The oocyst releases sporozoites that migrate to the mosquito's salivary glands, ready to infect a new host.
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 \(P,O,Q\).