Question

If the eccentricity of an ellipse is $\frac{5}{8}$ and the distance between its foci is $10$, then find latus-rectum of the ellipse.

Answer 1

According to the given,$2c=10\Rightarrow c=\frac{10}{2}=5$

We know that eccentricity$=\frac{c}{a}$

$\Rightarrow \frac{5}{8}=\frac{5}{a}\Rightarrow a=8$

Also,$c^2=a^2-b^2$

$\Rightarrow b^2=a^2-c^2=8^2-5^2=64-25=39$

Length of the latus- rectum$=\frac{2b^2}{a}=\frac{2\times 39}{8}=\frac{39}{4}$