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,
$x=\pm \frac{a}{e}=\pm \frac{9}{\sqrt{13}}$