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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
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B
xy+1=0
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C
xy=5
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D
None of these
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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 bisector
Hence,
$$2x-y+4=-x+2y+1$$
$$3x=3y-3$$
$$x-y+1=0$$

Mathematics

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