Conic Sections Question 435
Question: The directrix of the hyperbola is $ \frac{x^{2}}{9}-\frac{y^{2}}{4}=1 $
[UPSEAT 2003]
Options:
A) $ x=9/\sqrt{13} $
B) $ y=9/\sqrt{13} $
C) $ x=6/\sqrt{13} $
D) $ y=6/\sqrt{13} $
Show Answer
Answer:
Correct Answer: A
Solution:
Directrix of hyperbola $ x=\frac{a}{e} $ , where $ e=\sqrt{\frac{b^{2}}{a^{2}}+\frac{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}} $
therefore $ x=\frac{9}{13} $
BETA
