Conic Sections Question 470
Question: The distance between the directrices of a rectangular hyperbola is 10 units, then distance between its foci is
[MP PET 2002]
Options:
A) $ 10\sqrt{2} $
B) 5
C) $ 5\sqrt{2} $
D) 20
Show Answer
Answer:
Correct Answer: D
Solution:
$ \because $ Distance between directrices $ =\frac{2a}{e} $ . $ \because $ Eccentricity of rectangular hyperbola $ =\sqrt{2} $ . Distance between directrics $ =\frac{2a}{\sqrt{2}} $ . Given that , $ \frac{2a}{\sqrt{2}}=10 $
therefore $ 2a=10\sqrt{2} $
Now, distance between foci $ =2ae=(10\sqrt{2})(\sqrt{2})=20. $
BETA
