Question

Two lines represented by the equation $x^2+xy+y^2=0$ are

• A. Coincident
• B. Parallel
• C. Mutually perpendicular
• D. Imaginary

Answer 1

The correct option is D

Imaginary

Find the nature of the lines :

Given,

$x^2+xy+y^2=0$

dividing the equation by $x^2$

$\Rightarrow 1+\frac{y}{x}+\frac{y^2}{x^2}=0$

$\Rightarrow 1+m+m^2=0$ [ $m=\frac{y}{x}$]

$$\begin{gathered} \Rightarrow m=\frac{-1\pm \sqrt{1-4}}{2} \\ \Rightarrow m=\frac{-1\pm \sqrt{-3}}{2} \end{gathered}$$

Here, the slopes are imaginary

So, the lines are imaginary.

Hence, the correct option is (D).