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General Solution of Trigonometric Equation

The bisector ...

Question

The bisector of the acute angle between the lines $3 x - 4 y + 7 = 0$ and $12 x + 5 y - 2 = 0$ is :

A

11 x + 3 y - 9 = 0

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B

21 x + 77 y - 101 = 0

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C

11 x - 3 y + 9 = 0

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D

None of these

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Solution

The correct option is D $11 x - 3 y + 9 = 0$
$L_{1} : 3 x - 4 y + 7 = 0$
$L_{2} : 12 x + 5 y - 2 = 0$
Check : $3 \times (- 12) + (- 4) \times (- 5) < 0$
Therefore, required equation is :
$\frac{3 x - 4 y + 7}{5} = \frac{- 12 x - 5 y + 2}{13}$

$11 x - 3 y + 9 = 0$

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