If one of the slopes of the pair of lines ax^ | vedclass

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(C) Let the slopes of the lines $ax^{2}+2hxy+by^{2}=0$ be $m_{1}$ and $m_{2}$.According to the problem,$m_{1} = nm_{2}$.We know that $m_{1}+m_{2} = -\

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$4nh^{2}=(n+1)^{2}ab$

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(C) Let the slopes of the lines $ax^{2}+2hxy+by^{2}=0$ be $m_{1}$ and $m_{2}$.According to the problem,$m_{1} = nm_{2}$.We know that $m_{1}+m_{2} = -\frac{2h}{b}$ and $m_{1}m_{2} = \frac{a}{b}$.Substituting $m_{1} = nm_{2}$ into the sum and product equations:$m_{2}(n+1) = -\frac{2h}{b} \implies m_{2} = -\frac{2h}{b(n+1)}$.$nm_{2}^{2} = \frac{a}{b}$.Substituting the value of $m_{2}$ into the product equation:$n \left( -\frac{2h}{b(n+1)} \right)^{2} = \frac{a}{b}$.$n \left( \frac{4h^{2}}{b^{2}(n+1)^{2}} \right) = \frac{a}{b}$.$4nh^{2} = ab(n+1)^{2}$.

If one of the slopes of the pair of lines $ax^{2}+2hxy+by^{2}=0$ is $n$ times the other,then

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