If slopes of lines represented by $K x^{2} + 5 x y + y^{2} = 0$ differ by $1$ then $K =$

2

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3

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6

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8

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Solution

The correct option is C $6$
$K x^{2} + 5 x y + y^{2} = 0$
$m_{1} + m_{2} = - 5, m_{1} m_{2} = K$
Also, $m_{1} - m_{2} = 1$ ...... [Given]
Now, $(m_{1} - m_{2})^{2} = (m_{1} + m_{2})^{2} - 4 m_{1} m_{2}$
$\Rightarrow 1 = 25 - 4 K \Rightarrow K = 6$

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