Question

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

• A. $\frac{39}{4}$
• B. $12$
• C. $15$
• D. $\frac{37}{2}$

Answer 1

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

$Eccentricitye=\frac{5}{8}Distancebetweenthefociis2aeOr,2ae=10Or,a=8\therefore b^2=a^2-{\left(ae\right)}^{2}Or,b^2=64-25Or,b^2=39Lengthoflatusrectumis\frac{2b^2}{a}\therefore Length=\frac{39}{4}$

Option [A]