Answer
$\frac{x^2}{25}+\frac{y^2}{5}=1$
Work Step by Step
Major axis: $Length=2a$
$2a=10$
$a=5$
Foci on x-axis: major axis is horizontal.
Use the point $(\sqrt 5,2)$.
Equation of the ellipse:
$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$
$\frac{(\sqrt 5)^2}{5^2}+\frac{2^2}{b^2}=1$
$\frac{1}{5}+\frac{4}{b^2}=1$
$\frac{4}{b^2}=1-\frac{1}{5}=\frac{4}{5}$
$4b^2=20$
$b^2=5$
$b=\sqrt 5$
$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$
$\frac{x^2}{5^2}+\frac{y^2}{(\sqrt 5)^2}=1$
$\frac{x^2}{25}+\frac{y^2}{5}=1$
