Pair Of Straight Lines Question 24
Question: If one of the lines given by $ 6x^{2}-xy+4cy^{2}=0 $ is $ 3x+4y=0 $ , then c equals
[AIEEE 2004]
Options:
A) - 3
B) - 1
C) 3
D) 1
Show Answer
Answer:
Correct Answer: A
Solution:
Given equation of pair of lines is $ 6x^{2}-xy+4cy^{2}=0 $ …(i)
Slope of line $ 3x+4y=0 $ is $ \frac{-3}{4}=m_1 $ (say)
Product of slopes of lines $ m_1m_2=\frac{a}{b}=\frac{6}{4c}=\frac{3}{2c} $
$ \therefore $ $ m_2=\frac{3/2c}{-3/4}=\frac{-2}{c} $ . Also, $ m_1+m_2=\frac{-2h}{b}=\frac{1}{4c} $
$ \Rightarrow \frac{-3}{4}-\frac{2}{c}=\frac{1}{4c}\Rightarrow -3c-8=1\Rightarrow c=-3 $ .
BETA
