Answer
a) See the explanation
b) See the explanation.
c) See the explanation.
Work Step by Step
a)
An ellipse in terms of foci can be defined as the set of locus of the points in a plane such that the difference of distance from the 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 $c^2=(a^2+b^2)$
c) From part b, we have
$\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$
whose aysmptotes are: $y=\pm \frac{b}{a}x$
