Ellipse
Eccentricity and Foci
JEE Main 2019
Grade 11
Question:
If the eccentricity of an ellipse is $5/8$ and the distance between its foci is $10$, then the length of the latus rectum of the ellipse is:
(1) $\frac{39}{4}$
(2) $\frac{39}{8}$
(3) $\frac{37}{4}$
(4) $\frac{37}{8}$
Step-by-Step Solution
Key Concept: $2c = 10 \Rightarrow c = 5$; $e = 5/8 \Rightarrow a = 8$; $b^2 = a^2 - c^2 = 64 - 25 = 39$. Latus rectum $= 2b^2/a = 78/8 = 39/4$.
The detailed step-by-step mathematical proof is available inside the Mathbee app workspace.
Correct Answer: (1)