Q. The directrix of the hyperbola $\frac{x^{2}}{9} - \frac{y^{2}}{4} = 1$ is
A) $y = \frac{6}{\sqrt{13}}$
B) $x = \frac{6}{\sqrt{13}}$
C) $y = \frac{9}{\sqrt{13}}$
D) $x = \frac{9}{\sqrt{13}}$
Explanation
(d)
Given hyperbola is $\frac{x^{2}}{9} - \frac{y^{2}}{4} = 1$
$\therefore\ e = \sqrt{\frac{a^{2} + b^{2}}{a^{2}}} = \sqrt{\frac{9 + 4}{9}} = \frac{\sqrt{13}}{3}$
$\therefore Directrices\ are\ x = - \frac{9}{\sqrt{13}}$ and $x = \frac{9}{\sqrt{13}}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.