If the sum of slopes of the pair of lines giv | vedclass

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

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$-2$

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(A) 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 $m_{1}$ and $m_{2}$ be the slopes of the lines. The sum of slopes is $m_{1} + m_{2} = -\frac{2h}{b} = -\frac{2h}{-7} = \frac{2h}{7}$. The product of slopes is $m_{1}m_{2} = \frac{a}{b} = \frac{4}{-7} = -\frac{4}{7}$. Given that the sum of slopes is equal to the product of slopes,we have $\frac{2h}{7} = -\frac{4}{7}$. Multiplying both sides by $7$,we get $2h = -4$,which implies $h = -2$.

If the sum of slopes of the pair of lines given by $4x^{2} + 2hxy - 7y^{2} = 0$ is equal to the product of the slopes,then $h$ is

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