Conic Sections Question 424
Question: The eccentricity of the hyperbola $ 4x^{2}-9y^{2}=16 $ , is
Options:
A) $ \frac{8}{3} $
B) $ \frac{5}{4} $
C) $ \frac{\sqrt{13}}{3} $
D) $ \frac{4}{3} $
Show Answer
Answer:
Correct Answer: C
Solution:
Given equation of hyperbola, $ \frac{x^{2}}{4}-\frac{y^{2}}{(16/9)}=1 $ , $ a=2,b=\frac{4}{3} $ . As we know, $ b^{2}=a^{2}(e^{2}-1) $
therefore $ \frac{16}{9}=4(e^{2}-1) $
therefore $ e^{2}=\frac{13}{9} $ ,
$ \therefore e=\frac{\sqrt{13}}{3} $ .
BETA
