Conic Sections Question 353
Question: The length of the latus rectum of an ellipse is $ \frac{1}{3} $ of the major axis. Its eccentricity is
[EAMCET 1991]
Options:
A) $ \frac{2}{3} $
B) $ \sqrt{\frac{2}{3}} $
C) $ \frac{5\times 4\times 3}{7^{3}} $
D) $ {{( \frac{3}{4} )}^{4}} $
Show Answer
Answer:
Correct Answer: B
Solution:
Latus rectum $ =1/3 $ (Major axis)
therefore $ \frac{2b^{2}}{a}=\frac{2a}{3} $
therefore $ a^{2}=3b^{2}=3a^{2}(1-e^{2}) $
therefore $ e=\sqrt{\frac{2}{3}} $ .
BETA
