Pair Of Straight Lines Question 55
Question: For what value of $ ‘p’ $ , $ y^{2}+xy+px^{2}-x-2y=0 $ represents two straight lines
[UPSEAT 2002]
Options:
A) 2
B) $ \frac{1}{3} $
C) $ \frac{1}{4} $
D) $ \frac{1}{2} $
Show Answer
Answer:
Correct Answer: C
Solution:
For this to represent straight lines $ abc+2fgh-af^{2}-bg^{2}-ch^{2}=0 $
Therefore $ p^{2}+2(-1)( \frac{-1}{2} )( \frac{1}{2} )-p(1)-1( \frac{1}{4} )-p( \frac{1}{4} ) $
Therefore $ p^{2}+\frac{1}{2}-p-\frac{1}{4}-\frac{p}{4}=0 $
Therefore $ p^{2}-\frac{5p}{4}+\frac{1}{4}=0 $
Therefore $ 4p^{2}-5p+1=0 $
Therefore $ 4p^{2}-4p-p+1=0 $
Therefore $ (4p-1)(p-1)=0 $
Therefore $ p=\frac{1}{4},1. $
BETA
