Answer
(a)
Vertices: $V(±2,0)$
Foci: $F(±\sqrt 2,0)$
Eccentricity:
$e=\frac{\sqrt 2}{2}$
(b)
Length of the major axis:
$2a=4$
Length of the minor axis:
$2b=2\sqrt 2$
(c)
Work Step by Step
$x^2=4-2y^2$
$x^2+2y^2=4$
$\frac{x^2}{4}+\frac{y^2}{2}=1$
$\frac{x^2}{2^2}+\frac{y^2}{(\sqrt 2)^2}=1$
The major axis is horizontal.
Equation of an ellipse when major axis is horizontal (center at the origin):
$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$
So:
$a=2$
$b=\sqrt 2$
$c^2=a^2-b^2=4-2=2$
$c=\sqrt 2$
(a)
Vertices: $V(±a,0)=V(±2,0)$
Foci: $F(±c,0)=F(±\sqrt 2,0)$
Eccentricity:
$e=\frac{c}{a}=\frac{\sqrt 2}{2}$
(b)
Length of the major axis:
$2a=4$
Length of the minor axis:
$2b=2\sqrt 2$
