Three crosses were carried out in pea plants with respect to flower colour violet/white (V/v) and flower position axial/terminal (A/a). Study in the table the crosses ‘a’, ‘b’ and ‘c’ where parental phenotypes and their $F_1$ progeny phenotypes are given.
Find the genotypes of each of the parental pairs of crosses ‘a’, ‘b’ and ‘c’. 
(a) Cross: Violet, axial × White, axial Genotype of parents: $VvAa \times vvAa$ Explanation: $6/16$ Violet, axial: $VvAa$ $2/16$ White, terminal: $vvAa$ $6/16$ Violet, axial: $VvAa$ $2/16$ Violet, axial: $VvAa$
(b) Cross: Violet, axial × White, terminal Genotype of parents: $VvAa \times vvaa$ Explanation: $1/4$ Violet, axial: $VvAa$ $1/4$ Violet, terminal: $Vvaa$ $1/4$ White, axial: $vvAa$ $1/4$ White, terminal: $vvaa$
(c) Cross: Violet, axial × Violet, axial Genotype of parents: $VvAa \times VvAa$ Explanation: $3/4$ Violet, axial: $VvAa$ $1/4$ White, axial: $vvAa$
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 \(P,O,Q\).