Conic-Sections Question 588
Question: If the latus rectum of an ellipse is equal to one half its minor axis, what is the eccentricity of the ellipse?
Options:
A) $ \frac{1}{2} $
B) $ \frac{\sqrt{3}}{2} $
C) $ \frac{3}{4} $
D) $ \frac{\sqrt{15}}{4} $
Show Answer
Answer:
Correct Answer: B
Solution:
[b] Length of latus rectum of an ellipse is $ \frac{2b^{2}}{a} $ Where b is semi minor axis and a is semi- major axis. As given, $ \frac{2b^{2}}{a}=b $
$ \Rightarrow 2b=a\Rightarrow \frac{b}{a}=\frac{1}{2} $ We know that eccentricity $ e=\sqrt{1-\frac{b^{2}}{a^{2}}} $ $ =\sqrt{1-\frac{1}{4}}=\frac{\sqrt{3}}{2} $
BETA
