Answer
$\frac{x^2}{100}+\frac{y^2}{91}=1$
Work Step by Step
The endpoints of the major axis are the vertices.
$(±a,0)=(±10,0)$
$a=10$
The major axis is horizontal.
Foci: $(±c,0)$. So, the distance between foci is $c-(-c)=2c$
$2c=6$
$c=3$
$a^2=b^2+c^2$
$b^2=a^2-c^2=10^2-3^2=100-9=91$
$b=\sqrt {91}$
Equation of the ellipse:
$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$
$\frac{x^2}{10^2}+\frac{y^2}{(\sqrt {91})^2}=1$
$\frac{x^2}{100}+\frac{y^2}{91}=1$
