Question

find the bisector of angle between pair of lines in which the origin lies 4 x + 3 Y - 7 is equal to zero and 24 x + 7 Y - 31 is equal to zero.
​

Answer 1

Step-by-step explanation:

SWER

4x−3y+10=0 and 24x−7y+50=0

For origin to lie in obtuse traingle,

a

1

∗a

2

+b

1

∗b

2

>0

so,(4)(24)+(−3)(−7)>0

∴ origin lies in obtuse angle

Equation of the bisector of the angle in which origin lies is

5

4x−3y+10

=

25

24x−7y+50

i.e. 20x−15y=24x−7y i.e. 4x+8y=0

i.e. x+2y=0

Equation of the bisector of the angle in which origin does not lie is

20x−15y+50=−24x+7y−50 i.e. 44x−22y+100=0

i.e. 22x−11y+50=0

Distance of (2,1) from x+2y=0 is

5

4

Distance of (2,1) from 22x−11y+50=0 is

11

5

83

∴(2,1) lies in obtuse angle bisector