Consider the lines `L_(1) -=3x-4y+2=0 " and " L_(2)-=3y-4x-5=0.` Now, choose the correct statement(s).

Options

A. The line x+y=0 bisects the acute angle between `L_(1) "and " L_(2)` containing the origin.
B. The line x-y+1=0 bisects the obtuse angle between `L_(1) " and " L_(2)` not containing the origin.
C. The line x+y+3=0 bisects the obtuse angle between `L_(1) " and " L_(2)` containing the origin.
D. The line x-y+1=0 bisects the acute angle between `L_(1) " and " L_(2)` not containing the origin.

Answer

A, B

Explanation

We have `L_(1) -= 3x-4y+2=0`
`L_(2)-=4x-3y+5 =0`
Here, `a_(1)a_(2) + b_(1)b_(2) = (3)(4) + (-4)(-3) = 24 gt 0`
So, acute angle bisector is
3x-4y+2=4x-3y+5
or x+y+3=0
This bisector goes through the regions where expressions 3x-4y+2 and 4x-3y+5 have the same sign.
Also, this is the bisector of anlge which contains origin.