Question

The equation of lines parallel to $3x-4y-5=0$ at a unit distance from it is

• A. $3x-4y-10=0$
• B. $5x+3y-5=0$
• C. $3x+4y+10=0$
• D. $6x+2y+4=0$

Answer 1

Answer: (A)

$3x-4y-10=0$

Equation of line parallel to $3x-4y-5=0$ is given by, $3x-4y+c=0$
Also distance between given line is $1$

$\left|\frac{c_1-c_2}{\sqrt{a^2+b^2}}\right|$

$\Rightarrow \left|\frac{c+5}{\sqrt{3^2+4^2}}\right|=1$
$\Rightarrow |c+5|=5\Rightarrow c=0,-10$
Hence line parallel to $3x-4y-5=0$ and unit distance from it is
$3x-4y-10=0$ or $3x-4y=0$