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 $4x^2 + 2\lambda xy - 7y^2 = 0$. Comparing this with the general form $ax^2 + 2hxy + by^2 = 0$,we get $

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-$2$

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(C) The given equation of the pair of lines is $4x^2 + 2\lambda xy - 7y^2 = 0$. Comparing this with the general form $ax^2 + 2hxy + by^2 = 0$,we get $a = 4$,$2h = 2\lambda$,and $b = -7$. Let $m_1$ and $m_2$ be the slopes of the lines. The sum of the slopes is $m_1 + m_2 = \frac{-2h}{b} = \frac{-2\lambda}{-7} = \frac{2\lambda}{7}$. The product of the slopes is $m_1m_2 = \frac{a}{b} = \frac{4}{-7} = -\frac{4}{7}$. Given that the sum of the slopes is equal to the product of the slopes: $\frac{2\lambda}{7} = -\frac{4}{7}$. Multiplying both sides by $7$,we get $2\lambda = -4$. Therefore,$\lambda = -2$. Hence,option $C$ is correct.

If the sum of the slopes of the lines given by $4x^2 + 2\lambda xy - 7y^2 = 0$ is equal to the product of the slopes,then $\lambda$ is equal to

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