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The equation of the bisector of the acute angle between the lines $3 x-4 y+7=0$ and $12 x+5 y-2=0$ is
Option: 1
$21 x+77 y-101=0$

Option: 2
$11 x-3 y+9=0$

Option: 3
$31 x+77 y+101=0$

Option: 4
$11 x-3 y-9=0$

Answers (1)

best_answer

Bisector of the angles is given by $\frac{3 x-4 y+7}{5}= \pm \frac{12 x+5 y-2}{13}$

$\Rightarrow \quad 11 x-3 y+9=0$ $....(i)$

and $21 x+77 y-101=0$ $....(ii)$

Let the angle between the line $3 x-4 y+7=0$

and (i) is $\alpha$ , then

$\tan \alpha=\left|\frac{m_1-m_2}{1+m_1 m_2}\right|=\left|\frac{\frac{3}{4}-\frac{11}{3}}{1+\frac{3}{4} \times \frac{11}{3}}\right|=\frac{35}{45}<1 \Rightarrow \alpha<45^{\circ}$

Hence $11 x-3 y+9=0$ is the bisector of the acute angle between the given lines.

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vinayak

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