Answer
(a)
Vertices: $(0,±8)$
Foci: $(0,±\sqrt {55})$
Eccentricity:
$e=\frac{\sqrt {55}}{8}$
(b)
Length of the major axis:
$2a=16$
Length of the minor axis:
$2b=6$
(c)
Work Step by Step
$\frac{x^2}{9}+\frac{y^2}{64}=1$
$\frac{x^2}{3^2}+\frac{y^2}{8^2}=1$
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:
$a=8$
$b=3$
$c^2=a^2-b^2=8^2-3^2=64-9=55$
$c=\sqrt {55}$
(a)
Vertices: $(0,±a)=(0,±8)$
Foci: $(0,±c)=(0,±\sqrt {55})$
Eccentricity:
$e=\frac{c}{a}=\frac{\sqrt {55}}{8}$
(b)
Length of the major axis:
$2a=16$
Length of the minor axis:
$2b=6$
