1.

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

Answer»

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

Solution :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.


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