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(B) The given equation is $4x^2 + 2hxy - 7y^2 = 0$.Comparing this with the general form $ax^2 + 2hxy + by^2 = 0$,we have $a = 4$,$2h = 2h$,and $b = -7

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$-2$

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(B) The given equation is $4x^2 + 2hxy - 7y^2 = 0$.Comparing this with the general form $ax^2 + 2hxy + by^2 = 0$,we have $a = 4$,$2h = 2h$,and $b = -7$.Let the slopes of the lines be $m_1$ and $m_2$.Then,$m_1 + m_2 = -\frac{2h}{b} = -\frac{2h}{-7} = \frac{2h}{7}$ and $m_1m_2 = \frac{a}{b} = \frac{4}{-7} = -\frac{4}{7}$.Given that the sum and product of the slopes are equal,$m_1 + m_2 = m_1m_2$.Therefore,$\frac{2h}{7} = -\frac{4}{7}$.Multiplying both sides by $7$,we get $2h = -4$,which implies $h = -2$.

If the sum and product of the slopes of the lines represented by $4x^2 + 2hxy - 7y^2 = 0$ are equal,then $h = \dots$

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