Question

What is the equation of the bisectors of the angles between the lines represented by $x^2+2xycot\varnothing +y^2=0$?

• A. $x^2-y^2=0$
• B. $x^2-y^2=xy$
• C. $\left(x^2-y^2\right)cot\varnothing =2xy$
• D. None of these

Answer 1

The correct option is A

$x^2-y^2=0$

Explanation for correct answer :

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

Given, Equation of pair of straight lines is $x^2+2xycot\varnothing +y^2=0$.

We know that, the equation of straight lines is $x^2+2hxy+y^2=0$

Comparing both equations, we get

$a=1,b=1,h=cot\varnothing$

We know, equation of bisector is $\frac{x^2-y^2}{a-b}=\frac{xy}{h}$

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

Hence, the equation of the bisectors of the angles between the lines is $x^2-y^2=0$.

Thus, the correct answer is option(A).