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  4. 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

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Q. 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

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Solution:

after making constant terms positive, equation of lines are
$3 x-4 y+7=0 .....$ (i)
$-12 x-5 y+2=0 .....$ (ii)
$\because a_1 a_2+b_1 b_2=-36+20<0 $
$\therefore $ equation of acute angle bisector is
$\frac{3 x-4 y+7}{5} =+\frac{-12 x-5 y+2}{13}$
$\Rightarrow 11 x-3 y+9 =0$