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