The equation $x^{2} - 5 x y + 4 y^{2} = 0$ represents two lines passing through the origin which are

x - y = 0

x - 4 y = 0

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x + y = 0

x - 4 y = 0

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x - 5 y = 0

x + y = 0

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x - 2 y = 0

x - 3 y = 0

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Solution

The correct option is A $x - y = 0$ & $x - 4 y = 0$
$x^{2} - 5 x y + 4 y^{2} = 0 \Rightarrow x^{2} - 4 x y - x y + 4 y^{2} = 0 \Rightarrow (x - 4 y) (x - y) = 0$
Hence two lines are $x - y = 0$ and $x - 4 y = 0$ and both pass through origin.

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