Question

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

A
x+y+5=0
B
xy+1=0
C
xy=5
D
None of these

Solution

## The correct option is C $$x-y + 1= 0$$The equations are$$2x-y+4=0$$ and $$-x+2y+1=0$$Therefore the required angle bisector will be$$\dfrac{2x-y+4}{\sqrt{2^2+1}}=\pm\dfrac{-x+2y+1}{\sqrt{2^2+1}}$$Since, $$(2)(-1)+(-1)(2)=-4<0$$Therefore, positive will yield the equation of acute angle bisectorHence,$$2x-y+4=-x+2y+1$$$$3x=3y-3$$$$x-y+1=0$$Mathematics

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