Pair Of Straight Lines Question 47
Question: The equation $ x^{2}+kxy+y^{2}-5x-7y+6=0 $ represents a pair of straight lines, then k is
[MP PET 2000]
Options:
A) 5/3
B) 10/3
C) 3/2
D) 3/10
Show Answer
Answer:
Correct Answer: B
Solution:
$ \begin{vmatrix} 1 & k/2 & -5/2 \\ k/2 & 1 & -7/2 \\ -5/2 & -7/2 & 6 \\ \end{vmatrix} =0 $
$ \Rightarrow $ $ ( 6-\frac{49}{4} )-\frac{k}{2}( \frac{6k}{2}-\frac{35}{4} )-\frac{5}{2}( -\frac{7k}{4}+\frac{5}{2} )=0 $
Therefore $ 6k^{2}-35k+50=0 $
Therefore $ k=\frac{10}{3} $ .
BETA
