Conic Sections Question 149
Question: If the latus rectum of an ellipse be equal to half of its minor axis, then its eccentricity is
[MP PET 1991, 97; Karnataka CET 2000]
Options:
A) 3/2
B) $ \sqrt{3}/2 $
C) 2/3
D) $ \sqrt{2}/3 $
Show Answer
Answer:
Correct Answer: B
Solution:
$ \frac{2b^{2}}{a}=b $
therefore $ \frac{b}{a}=\frac{1}{2} $
therefore $ \frac{b^{2}}{a^{2}}=\frac{1}{4} $
Hence $ e=\sqrt{1-\frac{b^{2}}{a^{2}}}=\frac{\sqrt{3}}{2} $ .
BETA
