Question

In an ellipse, the distance between its focii is $6$ and minor axis is $8$. Then its' eccentricity is

• A. $\frac{3}{5}$
• B. $\frac{1}{2}$
• C. $\frac{4}{5}$
• D. $\frac{1}{\sqrt{5}}$

Answer 1

The correct option is A $\frac{3}{5}$

Given distance between foci of an ellipse $=6\Rightarrow 2ae=6\Rightarrow ae=3$
Also minor axis $=2b=8\Rightarrow b=4$
Now, $b^2=a^2(1-e^2)$
$\Rightarrow 16=a^2-a^2{e}^2\Rightarrow a^2=16+9=25\therefore a=5$ $\Rightarrow e=\frac{3}{a}=\frac{3}{5}$