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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