Directrix of hyperbola is frac{{{x^2}}}{9} - frac{{{y^2}}}{4} = 1

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10-2. Parabola, Ellipse, Hyperbola

easy

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

A

$x = 9/\sqrt {13} $

B

$y = 9/\sqrt {13} $

C

$x = 6/\sqrt {13} $

D

$y = 6/\sqrt {13} $

Solution

(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} $

Standard 11

Mathematics

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