Conic Sections Question 258
Question: The straight line $ x+y=\sqrt{2}p $ will touch the hyperbola $ 4x^{2}-9y^{2}=36 $ , if
[Orissa JEE 2003]
Options:
A) $ p^{2}=2 $
B) $ p^{2}=5 $
C) $ 5p^{2}=2 $
D) $ 2p^{2}=5 $
Show Answer
Answer:
Correct Answer: D
Solution:
The condition for the line $ y=mx+c $ will touch the hyperbola $ \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1 $ is $ c^{2}=a^{2}m^{2} $
$ -b^{2} $ Here $ m=-1 $ , $ c=\sqrt{2}p, $
$ a^{2}=9,b^{2}=4 $
We get $ 2p^{2}=5. $
BETA
