The equation of the bisector of the angle between the lines $2 x + y - 6 = 0$ and $2 x - 4 y + 7 = 0$ which contains the point $(1, 2)$ , is

6 x - 2 y - 5 = 0

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2 x + 6 y - 19 = 0

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6 x + 2 y - 5 = 0

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2 x + 6 y + 19 = 0

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Solution

The correct option is B $6 x - 2 y - 5 = 0$
Given lines are $l_{1} : 2 x + y - 6 = 0$ and $l_{2} : 2 x - 4 y + 7 = 0$
Rewritting the equation of lines,
$l_{1} : - 2 x - y + 6 = 0, l_{2} : 2 x - 4 y + 7 = 0$
Let $P = (1, 2)$
$l_{1} (P) \cdot l_{2} (P) = 2 \times 1 > 0$
The angle bisector containing the point $(1, 2)$ is given by
$\frac{- 2 x - y + 6}{\sqrt{(- 2)^{2} + (- 1)^{2}}} = + \frac{2 x - 4 y + 7}{\sqrt{2^{2} + (- 4)^{2}}} \Rightarrow 2 (- 2 x - y + 6) = 2 x - 4 y + 7 ∴ 6 x - 2 y - 5 = 0$

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