Pair Of Straight Lines Question 22
Question: If the equation $ \lambda x^{2}+2y^{2}-5xy+5x-7y+3=0 $ represents two straight lines, then the value of l will be
[RPET 1989]
Options:
A) 3
B) 2
C) 8
D) - 8
Show Answer
Answer:
Correct Answer: B
Solution:
$ abc+2fgh-af^{2}-bg^{2}-ch^{2}=0 $
$ \Rightarrow \lambda (2)(3)+2( \frac{-7}{2} )( \frac{5}{2} )( \frac{-5}{2} )-\lambda {{( \frac{-7}{2} )}^{2}} $
$ -2{{( \frac{5}{2} )}^{2}}-3{{( \frac{-5}{2} )}^{2}}=0 $
$ \Rightarrow 6\lambda +\frac{175}{4}-\frac{49}{4}\lambda -\frac{25}{2}-\frac{75}{4}=0 $
$ \Rightarrow 25\lambda =50\Rightarrow \lambda =2 $ .
BETA
