Answer
a) See the explanation
b) See the explanation.
Work Step by Step
a)
An ellipse in terms of foci can be defined as the set of locus points in a plane such that the sum of distance from each focus remains constant.
b)
The equation for the ellipse with foci $(\pm c,0)$ and vertices $(\pm a,0)$ is given by
$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$; $ a \geq b\gt 0$
and $c^2=(a^2-b^2)$
