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Question

The equation of the bisector of the angle between the lines 2x+y6=0 and 2x4y+7=0 which contains the point (1,2), is

A
6x2y5=0
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B
2x+6y19=0
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C
6x+2y5=0
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D
2x+6y+19=0
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Solution

The correct option is B 6x2y5=0
Given lines are l1:2x+y6=0 and l2:2x4y+7=0
Rewritting the equation of lines,
l1:2xy+6=0,l2:2x4y+7=0
Let P=(1,2)
l1(P)l2(P)=2×1>0
The angle bisector containing the point (1,2) is given by
2xy+6(2)2+(1)2=+2x4y+722+(4)22(2xy+6)=2x4y+76x2y5=0

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