Pair Of Straight Lines Question 143
Question: The value of $ \lambda , $ for which the equation $ x^{2}-y^{2}-x $ - $ \lambda y-2=0 $ represent a pair of straight line, are
[MP PET 2004]
Options:
A) 3, - 3
B) - 3, 1
C) 3, 1
D) -1, 1
Show Answer
Answer:
Correct Answer: A
Solution:
Given equation is $ x^{2}-y^{2}-x-\lambda y-2=0 $ .
Here, $ a=1 $ , $ b=-1 $ , $ c=-2 $ , $ h=0 $ , $ g=\frac{-1}{2} $ , $ f=\frac{-\lambda }{2} $ .
This equation represents a pair of straight line, if $ abc+2fgh-af^{2}-bg^{2}-ch^{2}=0 $
$ 2-\frac{{{\lambda }^{2}}}{4}+\frac{1}{4}=0 $
Therefore $ \frac{{{\lambda }^{2}}}{4}=\frac{9}{4}\Rightarrow {{\lambda }^{2}}=9,\lambda =\pm 3, $ i.e., (3, - 3).
BETA
