The parametric representation of a point on the ellipse whose foci are (-1, 0) and (7, 0) and eccentricity 1/2, is

Distance between two foci = 8

$\Rightarrow 2ae=8\Rightarrow ae=4\Rightarrow a=8(\because e=\frac{1}{2})$

Now, $b^2=a^2\left(1-e^2\right)\Rightarrow b^2=48\Rightarrow b=4\sqrt{3}$

The centre of the ellipse is the mid-point of the line joining two focus

Therefore, the coordinates of the centre are (3, 0). So, the

equation of the ellipse is

$\frac{(x-3{)}^2}{8^2}+\frac{(y-0{)}^2}{(4\sqrt{3}{)}^2}=1$

Hence, the parametric coordinates of a point on (i) are

$(3+8\cos \theta , 4\sqrt{3}\sin \theta )$