Conic Sections Question 376
Question: The eccentricity of the ellipse $ 4x^{2}+9y^{2}=36 $ , is
[MP PET 2000]
Options:
A) $ \frac{1}{2\sqrt{3}} $
B) $ \frac{1}{\sqrt{3}} $
C) $ \frac{\sqrt{5}}{3} $
D) $ \frac{\sqrt{5}}{6} $
Show Answer
Answer:
Correct Answer: C
Solution:
$ 4x^{2}+9y^{2}=36 $
$ \Rightarrow \frac{x^{2}}{9}+\frac{y^{2}}{4}=1 $ . Here, $ a^{2}=9,b^{2}=4 $
Now $ b^{2}=a^{2}(1-e^{2}) $ ,$ \frac{4}{9}=1-e^{2} $
$ \Rightarrow e=\frac{\sqrt{5}}{3} $ .
BETA
