Understanding the Plasmodium life cycle is crucial for malaria prevention and treatment strategies.
The life cycle of Plasmodium: Sporozoites enter the human bloodstream via a mosquito bite and infect liver cells. They multiply in liver cells to form merozoites, which are released into the bloodstream. Merozoites infect red blood cells, multiply, and cause cell rupture. Gametocytes are formed and circulate in the blood. When a mosquito bites, gametocytes are taken up, continuing the cycle.
The life cycle of Plasmodium: Sporozoites enter the human bloodstream via a mosquito bite and infect liver cells. They multiply in liver cells to form merozoites, which are released into the bloodstream. Merozoites infect red blood cells, multiply, and cause cell rupture. Gametocytes are formed and circulate in the blood. When a mosquito bites, gametocytes are taken up, continuing the cycle.
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 \(P,O,Q\).