The equation of the bisector of the obtuse angle between the lines `x-2y+4=0` and `4x-3y+2=0` is

Explanation

Equation of bisectors

`(x-2y+4)/sqrt5=(4x--3y+2)/sqrt(4^2+3^2)`

`sqrt5x-2sqrt5y+4sqrt5=4x-3y+2`

`y(3-2sqrt5)+x(sqrt5-4)+4sqrt5-2=0`

`m(beta_1)=(4-sqrt5)/(3-2sqrt5)`

this will be negative So, this is obtuse.

`(x-2y+4)/sqrt5=-(4x--3y+2)/sqrt(4^2+3^2)`

In this case it will be positive So, this is acue.
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