Answer
$\frac{x^2}{1}+\frac{y^2}{4}=1$
Work Step by Step
Foci on y-axis: major axis is vertical.
Major axis: $length=2a$
$2a=4$
$a=2$
$e=\frac{c}{a}$
$\frac{\sqrt 3}{2}=\frac{c}{2}$
$c=\sqrt 3$
$a^2=b^2+c^2$
$b^2=a^2-c^2=2^2-(\sqrt 3)^2=4-3=1$
$b=1$
Equation of the ellipse:
$\frac{x^2}{b^2}+\frac{y^2}{a^2}=1$
$\frac{x^2}{1^2}+\frac{y^2}{2^2}=1$
$\frac{x^2}{1}+\frac{y^2}{4}=1$
