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

2

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Solution

The correct option is A $2$
if $m_{1}$ and $m_{2}$ are slope of the lines, then by given condition $m_{1} + m_{2} = 4 m_{1} m_{2}$ $\Rightarrow - \frac{2 c}{7} = - \frac{4}{7} \Rightarrow c = 2$
By using $a x^{2} + 2 h x y + b y^{2} = 0$
$m_{1} + m_{2} = \frac{- 2 h}{b}$ and $m_{1} m_{2} = \frac{a}{b} .$

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