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Find the joint equation of bisector of the angles between the line represented by 5x2+6xy-y2=0

Find the joint equation of bisector of the angles between the line represented by 5x2+6xy-y2=0

Grade:11

1 Answers

Vikas TU
14149 Points
4 years ago
5x2+6xy-y2=0 
(5x-y)(x+y)=0 
5x-y=0,x+y=0 
Let P (x, y) be any point on one edge bisector. Since the focuses on the point bisectors are equi - inaccessible from both the lines, the separation of P (x, y) from the line (5x-y=0)= the separation of P (x, y) from the line (x + y = 0) 
5x-y/√25+1=x+y/√1+1 
5x-y/√26=x+y/√2 
(5x-y)2/26=(x+y)2/2 
2(5x-y)2=26(x+y)2 
2(25x2+y2-10xy)=26(x2+y2+2xy) 
50x2+2y2-20xy=26x2+26y2+52xy 
24x2-24y2-72xy=0 

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