Pair Of Straight Lines Question 49
Question: The equation $ 2x^{2}+4xy-ky^{2}+4x+2y-1=0 $ represents a pair of lines. The value of k is
[Karnataka CET 2001]
Options:
A) $ -\frac{5}{3} $
B) $ \frac{5}{3} $
C) $ \frac{1}{3} $
D) $ -\frac{1}{3} $
Show Answer
Answer:
Correct Answer: A
Solution:
Comparing the given equation with the standard equation, we get $ a=2,\ f=1,\ b=-k $ , $ g=2, $
$ c=-1 $ and $ h=2 $ .
Since equation represents a pair of lines, therefore $ abc+2fgh-af^{2}-bg^{2}-ch^{2}=0 $ or $ 2k+8-2+4k+4=0 $ or $ 6k=-10 $ .
Therefore $ k=-\frac{5}{3} $ .
BETA
