Answer
$x^2+ \frac{y^2}{4}=1$
Work Step by Step
RECALL:
The standard equation of an ellipse with whose center is at (0, 0) is:
(i) $\frac{x^2}{a^2} + \frac{y^2}{b^2}=1$ (horizontal major axis)
(ii) $\frac{x^2}{b^2} + \frac{y^2}{a^2}=1$ (vertical major axis)
where
$a \gt b$
2a = length of major axis
2b = length of minor axis
$a^2=b^2+c^2$
The foci are on the y-axis which means that the major axis of the ellipse is vertical.
The length of major axis is 4 $\longrightarrow 2a=4 \longrightarrow a=2$
The length of minor axis is 2 $\longrightarrow 2b=2 \longrightarrow b=1$
Therefore, the equation of the ellipse is:
$\\\frac{x^2}{b^2} + \frac{y^2}{a^2}=1
\\\frac{x^2}{1^2} + \frac{y^2}{2^2}=1
\\x^2 + \frac{y^2}{4} = 1$
