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

Question

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

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

Monjur Alahi

4 views

2025-01-04 04:42

1 Answers

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Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

Correct Answer - A::B
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.