Question

Find the equation for the ellipse that satisfies the given condition. Ends of major axis $(0,\pm \sqrt{5})$ ends of minor axis $(\pm 1,0)$

Answer 1

Equation of ellipse,

$\frac{x^2}{b^2}+\frac{y^2}{a^2}=1$

Given,

Ends of major axis: $(0,\pm \sqrt{5})$

$\Rightarrow a=\sqrt{5}$

Ends of minor axis: $(\pm 1,0)$

$\Rightarrow b=1$

Therefore, the equation is

$\frac{x^2}{1}+\frac{y^2}{5}=1$

Hence, this is the answer.