Question

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

Answer 1

It is given that, ends if major axis $(0,\pm \sqrt{5})$ and ends of minor axis $(\pm 1,0)$
Clearly, here the major axis is along the $y$-axis.
Therefore, the equation of the ellipse will be of the form $\frac{x^2}{b^2}+\frac{y^2}{a^2}=1$ where $a$ is the semi-major axis
Accordingly $a=\sqrt{5}$ and $b=1$
Thus, the equation of the ellipse is $\frac{x^2}{1^2}+\frac{y^2}{{\left(\sqrt{5}\right)}^2}=1$
$\Rightarrow \frac{x^2}{1}+\frac{y^2}{5}=1$