If the slope of one of the lines given by ax^ | vedclass

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(B) Let the slopes of the two lines be $m_1$ and $m_2$. Given $m_2 = 5m_1$.From the equation $ax^2 + 2hxy + by^2 = 0$,we have $m_1 + m_2 = -\frac{2h}{

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$5h^2 = 9ab$

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(B) Let the slopes of the two lines be $m_1$ and $m_2$. Given $m_2 = 5m_1$.From the equation $ax^2 + 2hxy + by^2 = 0$,we have $m_1 + m_2 = -\frac{2h}{b}$ and $m_1 m_2 = \frac{a}{b}$.Substituting $m_2 = 5m_1$ into the sum: $m_1 + 5m_1 = 6m_1 = -\frac{2h}{b} \implies m_1 = -\frac{h}{3b}$.Substituting $m_2 = 5m_1$ into the product: $m_1(5m_1) = 5m_1^2 = \frac{a}{b} \implies m_1^2 = \frac{a}{5b}$.Equating the square of the expression for $m_1$: $(-\frac{h}{3b})^2 = \frac{a}{5b} \implies \frac{h^2}{9b^2} = \frac{a}{5b}$.Multiplying both sides by $45b^2$: $5h^2 = 9ab$.

If the slope of one of the lines given by $ax^2 + 2hxy + by^2 = 0$ is $5$ times the other,then

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