Conic Sections Question 348
Question: Eccentricity of the ellipse whose latus rectum is equal to the distance between two focus points, is
Options:
A) $ \frac{\sqrt{5}+1}{2} $
B) $ \frac{\sqrt{5}-1}{2} $
C) $ \frac{\sqrt{5}}{2} $
D) $ \frac{\sqrt{3}}{2} $
Show Answer
Answer:
Correct Answer: B
Solution:
$ \frac{2b^{2}}{a}=2ae $
therefore $ b^{2}=a^{2}e $ or $ e=\frac{b^{2}}{a^{2}} $
Also $ e=\sqrt{1-\frac{b^{2}}{a^{2}}} $ or $ e^{2}=1-e $ or $ e^{2}+e-1=0 $
Therefore $ e=\frac{-1\pm \sqrt{5}}{2} $ . As $ e<1, $ $ e=\frac{\sqrt{5}-1}{2} $ .
BETA
