Question

For an ellipse the distance between its foci is $6$ and its minor axis is $8$, then its eccentricity is

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

Answer 1

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

Given,

$2ae=6$
$2b=8$
$b=a\sqrt{1-e^2}$..................(using the relation of a,b and e)
$\frac{e}{\sqrt{1-e^2}}=\frac{3}{4}$
$16e^2=9-9e^2$
$25e^2=9$
$\Rightarrow e=\frac{3}{5}$