Answer
$\frac{x^2}{25}+\frac{y^2}{16}=1$
Work Step by Step
Major axis is horizontal.
Equation of the ellipse:
$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$
The ellipse passes through the point $(5,0)$
$\frac{5^2}{a^2}+\frac{0^2}{b^2}=1$
$5^2=a^2$
$a=5$
The ellipse passes through the point $(0,4)$
$\frac{0^2}{a^2}+\frac{4^2}{b^2}=1$
$4^2=b^2$
$b=4$
$\frac{x^2}{5^2}+\frac{y^2}{4^2}=1$
$\frac{x^2}{25}+\frac{y^2}{16}=1$
