Conic Sections Question 455
Question: The equation of the hyperbola referred to its axes as axes of coordinate and whose distance between the foci is 16 and eccentricity is $ \sqrt{2} $ , is
[MNR 1984]
Options:
A) $ x^{2}-y^{2}=16 $
B) $ x^{2}-y^{2}=32 $
C) $ x^{2}-2y^{2}=16 $
D) $ y^{2}-x^{2}=16 $
Show Answer
Answer:
Correct Answer: B
Solution:
$ 2ae=16, $
$ e=\sqrt{2} $
therefore $ a=4\sqrt{2} $ and $ b=4\sqrt{2} $ equation is $ \frac{x^{2}}{{{(4\sqrt{2})}^{2}}}-\frac{y^{2}}{{{(4\sqrt{2})}^{2}}}=1 $
therefore $ x^{2}-y^{2}=32 $ .
BETA
