Conic Sections Question 438

Question: The eccentricity of the hyperbola $ 2x^{2}-y^{2}=6 $ is

[MP PET 1992]

Options:

A) $ \sqrt{2} $

B) 2

C) 3

D) $ \sqrt{3} $

Show Answer

Answer:

Correct Answer: D

Solution:

$ \frac{x^{2}}{(6/2)}-\frac{y^{2}}{6}=1 $

therefore $ a^{2}=3 $ and $ b^{2}=6 $

Therefore $ e=\sqrt{\frac{b^{2}}{a^{2}}+1} $

therefore $ e=\sqrt{3} $ .