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

Options

A. `x-2y+1=0`
B. `x-2y-2=0`
C. `x-2y-1=0`
D. none of these

Answer

C

Explanation

We have
`a(x-1)^(2)+2h(x-1)(y-0)+b(y-0)^(2)=0`
Clearly, it represents a pair of straight lines passing through (1, 0). Since the bisectors 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, is equation is
`y-0=(1)/(2)(x-1)rArrx-2y-1=0`.