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