Answer
(a)
Vertices: $(0,±9)$
Foci: $(0,±3\sqrt 5)$
Eccentricity:
$e=\frac{\sqrt 5}{3}$
(b)
Length of the major axis:
$2a=18$
Length of the minor axis:
$2b=12$
(c)
Work Step by Step
$\frac{x^2}{36}+\frac{y^2}{81}=1$
$\frac{x^2}{6^2}+\frac{y^2}{9^2}=1$
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:
$a=9$
$b=6$
$c^2=a^2-b^2=9^2-6^2=81-36=45$
$c=3\sqrt 5$
(a)
Vertices: $(0,±a)=(0,±9)$
Foci: $(0,±c)=(0,±3\sqrt 5)$
Eccentricity:
$e=\frac{c}{a}=\frac{3\sqrt 5}{9}=\frac{\sqrt 5}{3}$
(b)
Length of the major axis:
$2a=18$
Length of the minor axis:
$2b=12$
