Pair Of Straight Lines Question 52
Question: The value of k so that the equation $ 2x^{2}+5xy+3y^{2}+6x+7y+k=0 $ represents a pair of straight lines, is
[Kurukshetra CEE 2002]
Options:
A) 4
B) 6
C) 0
D) 8
Show Answer
Answer:
Correct Answer: A
Solution:
$ \begin{vmatrix} 2 & 5/2 & 3 \\ 5/2 & 3 & 7/2 \\ 3 & 7/2 & k \\ \end{vmatrix} =0 $
Therefore $ \begin{vmatrix} 4 & 5 & 6 \\ 5 & 6 & 7 \\ 6 & 7 & 2k \\ \end{vmatrix} =0 $
Therefore $ 4(12k-49)-5(10k-42)+6(35-36)=0 $
Therefore $ 48k-196-50k+210+210-216=0 $
Therefore $ k=4 $ .
BETA
