The directrix of the hyperbola is x^2 9 - y^2 4 = 1 - Vidyadip

MCQ

The directrix of the hyperbola is $\frac{{{x^2}}}{9} - \frac{{{y^2}}}{4} = 1$

✓
$x = 9/\sqrt {13} $
B
$y = 9/\sqrt {13} $
C
$x = 6/\sqrt {13} $
D
$y = 6/\sqrt {13} $

✓

Answer

Correct option: A.

$x = 9/\sqrt {13} $

a
(a) Directrix of hyperbola $x = \frac{a}{e}$,

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

Directrix is, $x = \frac{{{a^2}}}{{\sqrt {{a^2} + {b^2}} }} = \frac{9}{{\sqrt {9 + 4} }}$

==> $x = 9/\sqrt {13} $

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