Conic Sections Question 425
Question: The eccentricity of the conic $ x^{2}-4y^{2}=1 $ , is
[MP PET 1999]
Options:
A) $ \frac{2}{\sqrt{3}} $
B) $ \frac{\sqrt{3}}{2} $
C) $ \frac{2}{\sqrt{5}} $
D) $ \frac{\sqrt{5}}{2} $
Show Answer
Answer:
Correct Answer: D
Solution:
Given conic is $ \frac{x^{2}}{{{(1)}^{2}}}-\frac{y^{2}}{{{( \frac{1}{2} )}^{2}}}=1 $
$ \therefore b^{2}=a^{2}(e^{2}-1) $
therefore $ \frac{1}{4}+1=e^{2} $
therefore $ e=\frac{\sqrt{5}}{2} $ .
BETA
