A) coincident
B) parallel
C) mutually perpendicular
D) imaginary
Correct Answer: D
Solution :
Given pair of lines are \[{{x}^{2}}+xy+{{y}^{2}}=0\] This is a quadratic equation in \[x\] \[\therefore \] \[x=\frac{-y\pm \sqrt{{{y}^{2}}-4{{y}^{2}}}}{2}=y\left( \frac{-1\pm \sqrt{3}i}{2} \right)\] \[\Rightarrow \]\[x=\omega y\]and \[x={{\omega }^{2}}y\] Where \[\omega ,{{\omega }^{2}}\]are the cube roots of unity \[\Rightarrow \] \[(x-\omega y)(x-{{\omega }^{2}}y)=0\] \[\therefore \] The given lines are imaginary.
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