If the sum of the slopes of the lines given by $x^{2} - 2 c x y - 7 y^{2} = 0$ is four times their product, then $c$ has the value:

1

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Solution

The correct option is B $2$
The given pair of line $x^{2} - 2 c x y - 7 y^{2} = 0$
On comparing with ${a x}^{2} + 2 h x y + b y^{2} = 0$
we get $a = 1, 2 h = - 2 c, b = - 7$
$m_{1} + m_{2} = \frac{- 2 h}{b} = \frac{- 2 c}{7}, m_{1} m_{2} = \frac{a}{b} = - \frac{1}{7}$
Given $m_{1} + m_{2} = 4 m_{1} m_{2} \Rightarrow c = 2$

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