Lines are drawn parallel to the line `4x-3y+2=0`, at a distance `(3)/(5)` from the origin. Then which one of the following points lies on any of these lines ?

Options

A. `(-(1)/(4), (2)/(3))`
B. `(-(1)/(4), -(2)/(3))`
C. `((1)/(4), -(1)/(3))`
D. `((1)/(4), (1)/(3))`

Answer

A

Explanation

`4x -3y + 2 = 0`
Equation of line parallel to this line
`4x -3y + lamda = 0`
Distance of this line from origin.
`(|lamda|)/(cancel(5)) = (3)/(cancel(5)), lamda = +- 3`
Equation of lines will be
`4x -3y + 3 = 0` …(1)
and `4x -3y -3 = 0` …(2)
Option (1) is satisfying first line.