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The acute angle bisector between the lines $3 x - 4 y - 5 = 0, 5 x + 12 y - 26 = 0$ is

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$9 x - 3 y + 13 = 0$

$14 x - 112 y + 65 = 0$

$7 x - 56 y + 32 = 0$

$7 x - 13 y + 9 = 0$

answer is C.

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Detailed Solution

$a_{1} a_{2} + b_{1} b_{2} = - 32 < 0, c_{1} c_{2} = 130 > 0$

Use $\frac{a_{1} x + b_{1} y + c_{1}}{\sqrt{a_{1}^{2} + b_{1}^{2}}} = \frac{a_{2} x + b_{2} y + c_{2}}{\sqrt{a_{2}^{2} + b_{2}^{2}}}$

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