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One bisector of the angle between the li...

One bisector of the angle between the lines given by `a(x-1)^(2)+2h(x-1)y+by^(2)=0` is `2x+y-2=0`. The equation of the other bisector is

A

`x-2y+1=0`

B

`x-2y-2=0`

C

`x-2y-1=0`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
C
We have, `a(x-1)^2+2h(x-1)(y-1)(y-0)+b(y-0)^2=0` Clearly , it represents a pair of straight lines passing through `(1,0)`. Since , the bisector of the angles between two lines are always perpendicular . So, the other bisector passes through `(1,0)` and is perpendicular to `2x+y-2=0`. Hence its equation is `y-0=(1)/(2)(x-1)rArr x-2y-1=0" "[because ,=-2, "then"-(1)/(m)=(1)/(2)]`
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