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