Explanation

(a)
Given equation of ellipse is $\frac{x^{2}}{4} + \frac{y^{2}}{\frac{7}{4}} = 1$
Here, $a^{2} = 4,\ b^{2} = \frac{7}{4}$
$\mathbf{\therefore}b^{2} = a^{2}(1 - e^{2})$
$\Rightarrow \frac{7}{4} = 4\left( 1 - e^{2} \right)$
$\Rightarrow e^{2} = 1 - \frac{7}{16} = \frac{9}{16}$
$\Rightarrow e = \frac{3}{4}$
Thus, the foci are $\left( \pm \frac{3}{2},\ 0 \right)$
The radius of required circle $= \sqrt{\left( \frac{3}{2} - \frac{1}{2} \right)^{2} + (2 - 0)^{2}}$
$= \sqrt{1 + 4} = \sqrt{5}$