Question

In an ellipse the distance between its foci is 6 and its minor axis is 8 . Its eccentricity is

• A. $\frac{6}{5}$
• B. $\frac{4}{5}$
• C. $\frac{3}{5}$
• D. $\frac{3}{2}$

Answer 1

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

Given that $2ae=6$ and $2b=8$

$\Rightarrow ae=3$ $\Rightarrow b=4$

$b^2=a^2(1-e^2)$

$b^2=a^2-a^2{e}^2$

$16=a^2-9$

$\Rightarrow a^2=25$

$\Rightarrow a=5$

$5e=3$

$\Rightarrow e=\frac{3}{5}$.