The distance between the directrices of a rectangular hyperbola i… - Vidyadip

MCQ

The distance between the directrices of a rectangular hyperbola is $10$ units, then distance between its foci is

A
$10\sqrt 2 $
B
$5$
C
$5\sqrt 2 $
✓
$20$

✓

Answer

Correct option: D.

$20$

d
(d) Distance between directrices $ = \frac{{2a}}{e}$.

Eccentricity of rectangular hyperbola $ = \sqrt 2 $.

Distance between directrics $ = \frac{{2a}}{{\sqrt 2 }}$.

Given that , $\frac{{2a}}{{\sqrt 2 }} = 10$

==> $2a = 10\sqrt 2 $

Now, distance between foci $ = 2ae = (10\sqrt 2 )\,(\sqrt 2 ) = 20.$

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