Question

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

Answer 1

Ends of major axis $(0,\pm \sqrt{6})$ lies on y - axis .
So the equation of ellipse in standard form is,
$\frac{x^2}{b^2}+\frac{y^2}{a^2}=1$
now ends of major axis $(0,\pm a)$ is $(0,\pm \sqrt{5})$
$\Rightarrow a=\sqrt{5}$
Ends of minor axis $(\pm b,0)is(\pm 1,0)$ $\Rightarrow b=1$
Thus equation of required ellipse is,
$\frac{x^2}{1}+\frac{y^2}{5}=1$