The equation of the bisector of the angle between two lines $3 x - 4 y + 12 = 0$ and $12 x - 5 y + 7 = 0$ which contains the points $(- 1, 4)$ is-

21 x + 27 y + 121 = 0

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21 x - 27 y + 121 = 0

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21 x + 27 y + 191 = 0

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\frac{- 3 x + 4 y - 12}{5} = \frac{12 x - 5 y + 7}{13}

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Solution

The correct option is D $21 x - 27 y + 121 = 0$
Given two lines are $3 x - 4 y + 12 = 0, 12 x - 5 y + 7 = 0$
The angular bisectors will be $\frac{3 x - 4 y + 12}{5} = \pm \frac{12 x - 5 y + 7}{13}$
$65 x - 52 y + 156 = \pm (60 x - 25 y + 35)$
The equations of the angular bisectors are $5 x - 27 y + 121 = 0, 125 x - 77 y + 191 = 0$
$(- 1, 4)$ lies on the line $5 x - 27 y + 121 = 0$

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