Question

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

• A. $ y=6/\sqrt{13} $
• B. $ x=6/\sqrt{13} $
• C. $ y=9/\sqrt{13} $
• D. $ x=\pm 9/\sqrt{13} $

Answer 1

Answer: (D)

If the equation of hyperbola is
$\frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1$,
then equation of directrices are $x=\pm \frac{a}{e}$.
Given equation of hyperbola be $\frac{x^{2}}{9}-\frac{y^{2}}{4}=1$
Here, $a^{2}=9, b^{2}=4$
$ \therefore $ $e=\sqrt{1+\frac{b^{2}}{a^{2}}}=\sqrt{1+\frac{4}{9}} $
$\therefore $ Equation of directrices,
$x=\pm \frac{a}{e}=\pm \frac{9}{\sqrt{13}}$