The equation of the bisector of the acute angle between the lines 2x - y + 4 = 0 and x - 2y = 1 is

Clearly, from the figure, the origin is contained in the acute angle. Writing the equations of the lines as 2x - y + 4 = 0and -x + 2y + 1 = 0, here  a1a2+b1b2=2-1+-12=-4<0, the required acute angular  bisector is 2x−y+45=−x+2y+15  make c1 c2 >0 ,  1 if   a1a2+b1b2>0  then acute angular bisector isa1x+b1y+c1a21+b21=-a2x+b2y+c2a22+b22                                    2 if  a1a2+b1b2<0 then acute angular bisector is  a1x+b1y+c1a21+b21=+a2x+b2y+c2a22+b22