Answer
(a)
Vertices: $V(±10,0)$
Foci: $F(±6,0)$
Eccentricity:
$e=\frac{3}{5}$
(b)
Length of the major axis:
$2a=20$
Length of the minor axis:
$2b=16$
(c)
Work Step by Step
$16x^2+25y^2=1600$
$\frac{x^2}{100}+\frac{y^2}{64}1$
$\frac{x^2}{10^2}+\frac{y^2}{8^2}=1$
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:
$a=10$
$b=8$
$c^2=a^2-b^2=10^2-8^2=100-64=36$
$c=6$
(a)
Vertices: $V(±a,0)=V(±10,0)$
Foci: $F(±c,0)=F(±6,0)$
Eccentricity:
$e=\frac{c}{a}=\frac{6}{10}=\frac{3}{5}$
(b)
Length of the major axis:
$2a=20$
Length of the minor axis:
$2b=16$
