The equation $x^{3} + x^{2} y - x y^{2} - y^{3} - x^{2} + y^{2} = 0$ represents three lines.

Two of which are parallel

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Two of which are perpendicular

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all of which are concurrent

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which do not form a triangle

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Solution

The correct options are
A Two of which are parallel
B Two of which are perpendicular
D which do not form a triangle
$x^{3} + x^{2} y - x y^{2} - y^{3} - x^{2} + y^{2} = 0 \Rightarrow (x - y) (x + y) (x + y - 1) = 0$
Where $x + y = 0$ and $x + y - 1 = 0$ are parallel
$x + y = 0$ and $x + y - 1 = 0$ are perpendicular to $x - y = 0$
Two line are parallel hence does not form triangle

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