Question

One bisector of the angle between the lines given by $a{(x-1)}^2+2h(x-1)y+b{y}^2=0\text{is}2x+y-2=0$.The other bisector is

• A. $x–2y+1=0$
• B. $2x+y–1=0$
• C. $x+2y–1=0$
• D. $x–2y–1=0$

Answer 1

The correct option is D

$x–2y–1=0$

Explanation for the correct option:

Finding the other bisector:

Given: Line $a{(x-1)}^2+2h(x-1)y+b{y}^2=0$

Also angle bisector $2x+y-2=0$

The bisectors between two lines will be perpendicular to each other.

Slope of the given bisector is$-2.$

The other bisector will have slope $\frac{1}{2}$ and will pass through the point $(1,0).$

So equation is $y–y_1=m(x–x_1)$

$$\begin{gathered} \Rightarrow y–0=\frac{1}{2}(x–1) \\ \Rightarrow 2y=x–1 \\ \Rightarrow x–2y–1=0 \end{gathered}$$

Hence the correct answer is option (D).