lf $a x^{2} - 4 x y + y^{2} = 0$ represents two straight lines such that the slope of one of them is thrice the slope of the other, then the value of $a$ is

1

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Solution

The correct option is B $3$
Let the equation $a x^{2} - 4 x y + y^{2} = 0$ represents the lines $y - m_{1} x = 0$ and $y - m_{2} x = 0$
Given $m_{2} = 3 m_{1}$
$\Rightarrow a x^{2} - 4 x y + y^{2} = (y - m_{1} x) (y - 3 m_{1} x)$
$\Rightarrow a x^{2} - 4 x y + y^{2} = 3 m_{1}^{2} x^{2} - 4 m_{1} x y + y^{2}$
On comparing, we get
$m_{1} = 1$ and $a = 3 m_{1}^{2}$
$\Rightarrow a = 3$

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