Answer
(a)
Vertices: $V(0,±3)$
Foci: $F(0,±\sqrt 6)$
Eccentricity:
$e=\frac{\sqrt 6}{3}$
(b)
Length of the major axis:
$2a=6$
Length of the minor axis:
$2b=2\sqrt 3$
(c)
Work Step by Step
$3x^2+y^2=9$
$\frac{x^2}{3}+\frac{y^2}{9}=1$
$\frac{x^2}{(\sqrt 3)^2}+\frac{y^2}{3^2}=1$
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:
$a=3$
$b=\sqrt 3$
$c^2=a^2-b^2=3^2-(\sqrt 3)^2=9-3=6$
$c=\sqrt 6$
(a)
Vertices: $V(0,±a)=V(0,±3)$
Foci: $F(0,±c)=F(0,±\sqrt 6)$
Eccentricity:
$e=\frac{c}{a}=\frac{\sqrt 6}{3}$
(b)
Length of the major axis:
$2a=6$
Length of the minor axis:
$2b=2\sqrt 3$
