If the sum of the slopes of the lines given b | vedclass

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(C) The given equation of the pair of lines is ${x^2} - 2cxy - 7{y^2} = 0$.Comparing this with the general equation $ax^2 + 2hxy + by^2 = 0$,we have $

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$2$

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(C) The given equation of the pair of lines is ${x^2} - 2cxy - 7{y^2} = 0$.Comparing this with the general equation $ax^2 + 2hxy + by^2 = 0$,we have $a = 1$,$2h = -2c$,and $b = -7$.Let the slopes of the lines be $m_1$ and $m_2$.The sum of the slopes is $m_1 + m_2 = -\frac{2h}{b} = -\frac{-2c}{-7} = -\frac{2c}{7}$.The product of the slopes is $m_1m_2 = \frac{a}{b} = \frac{1}{-7} = -\frac{1}{7}$.According to the problem,the sum of the slopes is four times their product:$m_1 + m_2 = 4(m_1m_2)$$-\frac{2c}{7} = 4 	imes (-\frac{1}{7})$$-\frac{2c}{7} = -\frac{4}{7}$$2c = 4$$c = 2$.

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

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