Answer
$\frac{x^2}{256}+\frac{y^2}{48}=1$
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 $(16,0)$
$\frac{16^2}{a^2}+\frac{0^2}{b^2}=1$
$16^2=a^2$
$a=16$
The ellipse passes through the point $(8,6)$
$\frac{8^2}{16^2}+\frac{6^2}{b^2}=1$
$\frac{1}{4}+\frac{6^2}{b^2}=1$
$\frac{36}{b^2}=1-\frac{1}{4}=\frac{3}{4}$
$3b^2=144$
$b^2=48$
$\frac{x^2}{16^2}+\frac{y^2}{48}=1$
$\frac{x^2}{256}+\frac{y^2}{48}=1$
