Conic Sections Question 479
Question: The eccentricity of the hyperbola $ 5x^{2}-4y^{2}+20x+8y=4 $ is
[UPSEAT 2004]
Options:
A) $ \sqrt{2} $
B) $ \frac{3}{2} $
C) 2
D) 3
Show Answer
Answer:
Correct Answer: B
Solution:
Given equation of hyperbola is $ 5x^{2}-4y^{2}+20x+8y=4 $
$ 5{{(x+2)}^{2}}-4{{(y-1)}^{2}}=20 $
therefore $ \frac{{{(x+2)}^{2}}}{4}-\frac{{{(y-1)}^{2}}}{5}=1 $ From $ b^{2}=a^{2}(e^{2}-1) $ , $ 5=4(e^{2}-1) $
$ \Rightarrow e^{2}=9/4\Rightarrow e=3/2 $ .
BETA
