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

x + y + 5 = 0

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x - y + 1 = 0

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x - y + 5

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none of these

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Solution

The correct option is B $x - y + 1 = 0$
Since, $c_{1} c_{2} < 0$
i.e. $4 \times - 1 = - 4 < 0$
The equation of the bisector of the acute angle between the lines $2 x - y + 4 = 0$ and $x - 2 y - 1 = 0$ is $\frac{2 x - y + 4}{\sqrt{5}} + \frac{x - 2 y - 1}{\sqrt{5}} = 0$
$\Rightarrow x - y + 1 = 0$

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