Answer
$\frac{x^2}{36}+\frac{y^2}{21}=1$
Work Step by Step
Major axis is horizontal.
Foci: $(±c,0)=(±\sqrt {15},0)$
$c=\sqrt {15}$
Vertices: $(±a,0)=(±6,0)$
$a=6$
$a^2=b^2+c^2$
$b^2=a^2-c^2=6^2-(\sqrt {15})^2=36-15=21$
$b=\sqrt {21}$
Equation of the ellipse:
$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$
$\frac{x^2}{6^2}+\frac{y^2}{(\sqrt {21})^2}=1$
$\frac{x^2}{36}+\frac{y^2}{21}=1$
