Find the equations of lines parallel to `3x-4y-5=0` at a unit distance from it.

Explanation

Equation of line parallel to 3x−4y−5=0 is given by, 3x−4y+c=0

Also distance between given line is 1

`(c_1-c_2)/sqrt(a^2+b^2)=1`

⇒`(c+5)/sqrt(3^2+4^2)=1`

⇒`∣c+5∣=5⇒c=0,−10`

Hence line parallel to `3x−4y−5=0` and unit distance from it is

`3x−4y−10=0 or 3x−4y=0`