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The bisector of the acute angle between the lines 2 x -y - 4 =0 and X - 2y + +10=0 is

The bisector of the acute angle between the lines 2 x -y - 4 =0 and X - 2y + +10=0  is

Grade:11

1 Answers

Danish
16 Points
4 years ago
2x-y-4=0        eq-1
x-2y+10=0      eq-2
 
\frac{2x-y-4}{\sqrt{4+1}}=\pm \frac{x-2y+10}{\sqrt{1+4}}         eq. of angle bisectors
 
(If in this equation,
a1a2+b1b2>0 then -ve sign is for acute angle bisector and +ve sign is for obtuse angle bisector.
If, a1a2+b1b2
 
2*1+[-1*(-2)]     ( a1a2+b1b2)
=2+2
=4>0
 
so, we use -ve sign for acute angle bisector
2x-y-4=-(x-2y+10)
2x-y-4=-x+2y-10
3x-3y+6=0
x-y+2=0 is the required equation for acute angle bisector
 
 
 

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