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

Question

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

Accepted Answer

$2ae=6\Rightarrow ae=3$; $2b=8\Rightarrow b=4$. Using $b^2=a^2-a^2e^2=a^2-9$:
$$16=a^2-9\Rightarrow a^2=25\Rightarrow a=5\Rightarrow e=\frac{3}{5}.$$

Solutions · 1