Question

find the equation of two straight lines which are parallel to the straight line x + 7 y + 2=0 and a unit distance from the point (2, - 1)​

Answer 1

Answer: $x+7y+5(1+\sqrt{2})\ and\ x+7y+5(1-\sqrt{2})$

Explanation:

General equation of line parallel to the given line x+7y+2=0 is

x+7y+c=0

This line must be unit distance from point (2,-1)

Point (2,-1) may be either side of line so we can write

$\frac{\left | 2+7(-1)+c \right |}{\sqrt{1^2+7^2}}=1\\\frac{\left | c-5 \right |}{\sqrt{50}}=1\\\left | c-5 \right |=\sqrt{50}\\c-5=\pm\sqrt{50}=\pm5\sqrt{2}\\c=5\pm5\sqrt{2}$

So, there can be 2 line i.e.

$x+7y+5(1+\sqrt{2})\ and\ x+7y+5(1-\sqrt{2})$