Answer
(a)
Vertices: $V(0,±4)$
Foci: $F(0,±2\sqrt 3)$
Eccentricity:
$e=\frac{\sqrt 3}{2}$
(b)
Length of the major axis:
$2a=8$
Length of the minor axis:
$2b=4$
(c)
Work Step by Step
$4x^2+y^2=16$
$\frac{x^2}{4}+\frac{y^2}{16}=1$
$\frac{x^2}{2^2}+\frac{y^2}{4^2}=1$
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:
$a=4$
$b=2$
$c^2=a^2-b^2=4^2-2^2=16-4=12$
$c=2\sqrt 3$
(a)
Vertices: $V(0,±a)=V(0,±4)$
Foci: $F(0,±c)=F(0,±2\sqrt 3)$
Eccentricity:
$e=\frac{c}{a}=\frac{2\sqrt 3}{4}=\frac{\sqrt 3}{2}$
(b)
Length of the major axis:
$2a=8$
Length of the minor axis:
$2b=4$
