Find the equation of the lines bisecting the angles between the straight lines  3x-4y+10=0 and 5x-12y-10=0 writing first the bisector of the angle in which origin lies.

the answer will be removed with the help of a formula

 

There is a formula for removing the equation of the angle bisector of two straight

 

lines . It states as follows

 

If equation of two lines making any angle between them are:

 

a₁x + b₁y + c₁=0

 

a₂x + b₂y + c₂=0

 

Then the equation of the bisector of the angle between them will be:

 

(a₁x + b₁y + c₁) / ( a₁² + b₁² ) =  (a₂x + b₂y + c₂) / ( a₂² + b₂² )

 

After solving hte equation we will get two equations different.

 

But the equation that is formed  by taking + signis the real answer if you want

 

the equation of the bisector containing the origin.

 

And if in any of the equations the constant i.e 10 in this question is negative

then make it positve by multiplying -1 on both sides .

 

So,

 

The equation will be [ 64x - 112y + 80 = 0 ] in expansion form

 

and in its reduced form it will be [ 4x - 7y + 5 = 0 ]

 

Hence the answer.

 

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