Answer
$\frac{x^2}{25}+\frac{y^2}{9}=1$
Work Step by Step
Major axis is horizontal.
$(±5,0)=(±a,0)$
$a=5$
$e=\frac{c}{a}$
$\frac{4}{5}=\frac{c}{5}$
$5c=20$
$c=4$
$a^2=b^2+c^2$
$b^2=a^2-c^2=5^2-4^2=25-16=9$
$b=3$
Standard form when major axis is horizontal:
$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$
$\frac{x^2}{5^2}+\frac{y^2}{3^2}=1$
$\frac{x^2}{25}+\frac{y^2}{9}=1$
