Answer
$\frac{x^2}{7}+\frac{y^2}{16}=1$
Work Step by Step
Major axis is vertical.
Equation of the ellipse:
$\frac{x^2}{b^2}+\frac{y^2}{a^2}=1$
The ellipse passes through the point $(0,4)$
$\frac{0^2}{b^2}+\frac{4^2}{a^2}=1$
$4^2=a^2$
$a=4$
Foci: $(0,±c)=(0,±3)$
$c=3$
$a^2=b^2+c^2$
$b^2=a^2-c^2=4^2-3^2=16-9=7$
$b=\sqrt 7$
$\frac{x^2}{(\sqrt 7)^2}+\frac{y^2}{4^2}=1$
$\frac{x^2}{7}+\frac{y^2}{16}=1$
