Question

The eccentricity of the ellipse, whose end points of major axis and minor axis are $(\pm \sqrt{5},0)$ and $(0,\pm 1)$ respectively, is

• A. $\frac{\sqrt{3}}{2}$
• B. $\frac{1}{\sqrt{5}}$
• C. $\frac{1}{\sqrt{3}}$
• D. $\frac{2}{\sqrt{5}}$

Answer 1

The correct option is D $\frac{2}{\sqrt{5}}$

Since the ends of the major axis are $(\pm \sqrt{5},0)$
$\Rightarrow a=\sqrt{5}$

The ends of the minor axis are $(0,\pm 1)$
$\Rightarrow b=1$
Here, $a>b$
$\therefore e=\sqrt{1-\frac{b^2}{a^2}}\Rightarrow e=\frac{2}{\sqrt{5}}$