The general equation of a straight line parallel to the given line is

x + 2y + c = 0,

where "c" is some constant.


If we want our straight line be parallel to the given line and pass at the distance of 2 from the origin (x,y) = (0,0), 
we must find "c" from this equation


 = 2    (1)


(see the lesson The distance from a point to a straight line in a coordinate plane in this site).


From equation (1), |c| = ,  so c can have two values: c =   or  c = .


Thus, the two equations the problem asks for are

 = 0   (2)

and

 = 0   (3).