Pair Of Straight Lines Question 53
Question: If the equation $ 3x^{2}+xy-y^{2}-3x+6y+k=0 $ represents a pair of lines, then k is equal to
[Karnataka CET 2002]
Options:
A) 9
B) 1
C) 0
D) - 9
Show Answer
Answer:
Correct Answer: D
Solution:
$ \begin{vmatrix} 3 & 1/2 & -3/2 \\ 1/2 & -1 & 3 \\ -3/2 & 3 & k \\ \end{vmatrix} =0 $
Therefore $ \begin{vmatrix} 6 & 1 & -3 \\ 1 & -2 & 6 \\ -3 & 6 & 2k \\ \end{vmatrix} =0 $
Therefore $ 6(-4k-36)-1(2k+18)-3(6-6)=0 $
Therefore $ -24k-216-2k-18=0 $
Therefore $ k=-9 $ .
BETA
