Find the equations of two straight lines each of which is parallel to and at a distance of $\sqrt {5}$ from the line $x+2y-7=0$.
My Attempt: The equation of any line parallel to $x+2y-7=0$ is $x+2y+k=0$
The distance between these two lines is: $$d=\dfrac {|k+7|}{\sqrt {5}}$$
The equation of any line parallel to $x+2y-7=0$ is $x+2y+k=0$
The distance between these two lines is: $$d=\dfrac {|k+7|}{\sqrt {5}}$$
Put $d=\sqrt {5}$ ,
$$\sqrt {5}=\dfrac {|k+7|}{\sqrt {5}}$$
$5=|k+7|$
$k+7=5$ or $k+7=-5$
$k=-2$ or $k= -12$
Hence the equations of the two lines are $x+2y-2=0$ and $x+2y-12=0$