The difference of the slopes of the lines represented by $6 x^{2} - 5 x y + y^{2} = 0$ is

1

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2

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3

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4

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Solution

The correct option is C $1$
Given,
$6 x^{2} - 5 x y + y^{2} = 0$
$\Rightarrow 6 x^{2} + 2 (\frac{- 5}{2}) x y + y^{2} = 0$
$m_{1} + m_{2} = \frac{- 2 λ}{b} = \frac{5}{1} = 5$
$m_{1} + m_{2} = \frac{a}{b} = \frac{6}{1} = 6$
$(m_{1} - m_{2})^{2} = (m_{1} + m_{2})^{2} - 4 m_{1} m_{2}$
$= 25 - 24$
$\Rightarrow m_{1} - m_{2} = 1$ or $m_{1} - m_{2} = - 1$
$∴ m_{1} - m_{2} = 1$

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Equation $6 x^{2} - 5 x y + y^{2} = 0$ represents____________________

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