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  4. If the sum of the slopes of the lines given by x2 - 2cxy - 7y2 = 0 is four times their product, then the value of c is

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

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Solution:

Let the lines be $y = m_1 x$ and $y = m_2x$ then
$m_1 + m_2 = - \frac{2c}{7}$ and $m_1m_2 = - \frac{1}{7}$
Given $m_1 + m_2 = 4 \,m_1m_2$
$\Rightarrow - \frac{2c}{7} = - \frac{4}{7} $
$\Rightarrow c = 2$