Question

The equation of the line parallel to $5x-12y+26=0$ and at a distance of $4$ units from it, is

• A. $5x-12y-26=0$
• B. $5x-12y+26=0$
• C. $5x-12y-78=0$
• D. $5x-12y+78=0$

Answer 1

Answer: (C), (D)

The correct options are
C $5x-12y-78=0$
D $5x-12y+78=0$

Given equation of line is
$5x-12y+26=0$

Let the required equation of line parallel to the given line is
$5x-12y+c=0$

$d=\frac{|c-26|}{\sqrt{5^2+{12}^2}}=\frac{|c-26|}{13}=4$
$\Rightarrow |c-26|=52$

$\Rightarrow c-26=\pm 52$

$\Rightarrow c=-26,78$

Required equation of line is

$5x-12y-26=0$ and $5x-12y+78=0$