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# If the sum of the slopes of the lines given by $x^2-2cxy-7y^2=0$ is four times their product c has the value.

$\begin{array}{1 1}(A)\;-2\\(B)\;-1 \\(C)\;2\\(D)\;1 \end{array}$

Let the lines be $y=m_1X$
$y=m_2x$ then
$m_1+m_2=-\large\frac{-2c}{7}$
$m_1m_2=-\large\frac{1}{2}$
Given $m_1+m_2=4m_1m_2$
=> $\large\frac{2c}{7}=\frac{-4}{7}$
$2c=\large\frac{-28}{7}$
$2c=-4$
$c=-2$
$c=2$
Hence C is the correct answer.