Answer
$\frac{x^2}{39}+\frac{y^2}{49}=1$
Work Step by Step
Major axis is vertical.
Foci: $(0,±c)=(0,±\sqrt {10})$
$c=\sqrt {10}$
Vertices: $(0,±a)=(0,±7)$
$a=7$
$a^2=b^2+c^2$
$b^2=a^2-c^2=7^2-(\sqrt {10})^2=49-10=39$
$b=\sqrt {39}$
Equation of the ellipse:
$\frac{x^2}{b^2}+\frac{y^2}{a^2}=1$
$\frac{x^2}{(\sqrt {39})^2}+\frac{y^2}{7^2}=1$
$\frac{x^2}{39}+\frac{y^2}{49}=1$
