Question

What is the equation of the bisectors of the angle between the lines represented by the equation $x^2-y^2=0$?

• A. $x=0$
• B. $y=0$
• C. $xy=0$
• D. None of these

Answer 1

The correct option is C

$xy=0$

Explanation of correct answer :

Finding the equation of the bisectors of the angle between the lines :

Given, Equation of pair of lines, $x^2-y^2=0$

We know that, the equation of pair of straight lines is $a{x}^2+2hxy+b{y}^2$

On comparing both equations, we get,

$a=1,b=-1,h=0$

We know that angle bisector formula is $\frac{x^2-y^2}{a-b}=\frac{xy}{h}$

Put the values in the angle bisector formula,

$$\begin{gathered} \Rightarrow \frac{x^2-y^2}{1-\left(-1\right)}=\frac{xy}{0} \\ \Rightarrow 2xy=0\left(\text{cross-multiplying}\right) \\ \Rightarrow xy=0 \end{gathered}$$

Hence, the equation of the bisectors of the angle between the lines is $xy=0$

Hence,the correct answer is Option(C).