question_answer

Lines are drawn parallel to the line \[4x3y+2=0,\]at a distance \[\frac{3}{5}\]from the origin. Then which one of the following points lies on any of these lines? [JEE Main 10-4-2019 Afternoon]

A) \[\left( -\frac{1}{4},\frac{2}{3} \right)\]

B) \[\left( \frac{1}{4},\frac{1}{3} \right)\]

C) \[\left( -\frac{1}{4},-\frac{2}{3} \right)\]                   

D) \[\left( \frac{1}{4},-\frac{1}{3} \right)\]

Correct Answer: A

Solution :

Required line is\[4x-3y+\lambda =0\] \[\left| \frac{\lambda }{5} \right|=\frac{3}{5}\]             \[\Rightarrow \lambda =\pm 3.\]             So, required equation of line is \[4x3y+3=0\]and \[4x3y3=0\] [a] \[4\left( -\frac{1}{4} \right)-3\left( \frac{2}{3} \right)+3=0\]