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Bisectors of Angle between Two Lines

The equations...

Question

The equations of three lines are given by :
15x-8y+1=0 ,12x+5y-3=0 and 21x-y-2=0 .
Show that third line bisects angle between other two lines.

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Solution

L1 : 15x - 8y + 1 = 0
L2 : -12x - 5y +3 = 0
Check: 15 (-12)+(-8) (-5) <0
∴ Eqn. to acute angle bisector

$\frac{15 x - 8 y + 1}{17}$ = $\frac{- 12 x - 5 y + 3}{13}$

⇒195x-104y+13=-204x-85y+51
⇒399x-19y-38=0
⇒21x-y-2=0

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Bisectors of Angle between Two Lines

Standard XII Mathematics