Conic Sections Question 366
Question: The eccentricity of the ellipse $ 25x^{2}+16y^{2}=100 $ , is
Options:
A) $ \frac{5}{14} $
B) $ \frac{4}{5} $
C) $ \frac{3}{5} $
D) $ \frac{2}{5} $
Show Answer
Answer:
Correct Answer: C
Solution:
$ \frac{x^{2}}{4}+\frac{y^{2}}{(25/4)}=1 $ . Here, $ a=2,b=5/2 $
$ \therefore b>a $ , therefore $ a^{2}=b^{2}(1-e^{2}) $
therefore $ 4=\frac{25}{4}(1-e^{2}) $
therefore $ \frac{16}{25}=1-e^{2} $
therefore $ e^{2}=1-\frac{16}{25}=\frac{9}{25} $ , $ e=\frac{3}{5} $ .
BETA
