Answer
(a)
Vertices: $V(±a,0)=V(±5,0)$
Foci: $F(±c,0)=F(±\sqrt {21},0)$
Eccentricity:
$e=\frac{c}{a}=\frac{\sqrt {21}}{5}$
(b)
Length of the major axis:
$2a=10$
Length of the minor axis:
$2b=4$
(c)
Work Step by Step
$4x^2+25y^2=100$
$\frac{x^2}{25}+\frac{y^2}{4}1$
$\frac{x^2}{5^2}+\frac{y^2}{2^2}=1$
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:
$a=5$
$b=2$
$c^2=a^2-b^2=5^2-2^2=25-4=21$
$c=\sqrt {21}$
(a)
Vertices: $V(±a,0)=V(±5,0)$
Foci: $F(±c,0)=F(±\sqrt {21},0)$
Eccentricity:
$e=\frac{c}{a}=\frac{\sqrt {21}}{5}$
(b)
Length of the major axis:
$2a=10$
Length of the minor axis:
$2b=4$
