Question

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

• A. $\frac{39}{4}$
• B. $\frac{37}{6}$
• C. $\frac{43}{3}$
• D. none of these

Answer 1

The correct option is A $\frac{39}{4}$

Let the equation of the required ellipse be $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ and let e be its eccentricity.

We have,

$e=\frac{5}{8}$ and $2ae=10$

$e=\frac{5}{8}$ and $ae=5$

$e=\frac{5}{8}$ and $a=8$

Therefore,

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

$b^2=64(1-\frac{25}{64})=39$

Hence, length of the latusrectum = $\frac{2b^2}{a}=2\times \frac{39}{8}=\frac{39}{4}$