If the slopes of the lines represented by ax^ | vedclass

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(C) Let the slopes of the lines be $m_1 = m$ and $m_2 = 3m$.From the equation $ax^{2} + 2hxy + by^{2} = 0$,we have the sum of slopes $m_1 + m_2 = -\fr

Vedclass · Accepted Answer

$4/3$

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(C) Let the slopes of the lines be $m_1 = m$ and $m_2 = 3m$.From the equation $ax^{2} + 2hxy + by^{2} = 0$,we have the sum of slopes $m_1 + m_2 = -\frac{2h}{b}$ and the product of slopes $m_1 m_2 = \frac{a}{b}$.Substituting the values: $m + 3m = 4m = -\frac{2h}{b} \implies m = -\frac{h}{2b}$.Also,$m 	imes 3m = 3m^2 = \frac{a}{b}$.Substituting $m = -\frac{h}{2b}$ into the product equation: $3(-\frac{h}{2b})^2 = \frac{a}{b} \implies 3(\frac{h^2}{4b^2}) = \frac{a}{b}$.Simplifying,$\frac{3h^2}{4b^2} = \frac{a}{b} \implies \frac{h^2}{ab} = \frac{4}{3}$.Thus,$h^2 : ab = 4 : 3$ or $\frac{4}{3}$.

If the slopes of the lines represented by $ax^{2} + 2hxy + by^{2} = 0$ are in the ratio $1 : 3$,then $h^{2} : ab =$

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