If the slope of one line is twice the slope o | vedclass

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(B) Given the pair of straight lines $ax^2 + 2hxy + by^2 = 0$. Let the slopes of the lines be $m_1$ and $m_2$. Given $m_1 = 2m_2$ ...$(i)$ We know tha

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$9$

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(B) Given the pair of straight lines $ax^2 + 2hxy + by^2 = 0$. Let the slopes of the lines be $m_1$ and $m_2$. Given $m_1 = 2m_2$ ...$(i)$ We know that $m_1 + m_2 = -\frac{2h}{b}$ ...(ii) and $m_1 m_2 = \frac{a}{b}$ ...(iii) Substituting $(i)$ into (ii): $2m_2 + m_2 = -\frac{2h}{b} \implies 3m_2 = -\frac{2h}{b} \implies m_2 = -\frac{2h}{3b}$ ...(iv) Substituting $(i)$ into (iii): $2m_2 \cdot m_2 = \frac{a}{b} \implies 2m_2^2 = \frac{a}{b}$ ...$(v)$ Substituting (iv) into $(v)$: $2(-\frac{2h}{3b})^2 = \frac{a}{b} \implies 2 \cdot \frac{4h^2}{9b^2} = \frac{a}{b} \implies \frac{8h^2}{9b^2} = \frac{a}{b} \implies 8h^2 = 9ab$.

If the slope of one line is twice the slope of the other in the pair of straight lines $ax^2 + 2hxy + by^2 = 0$,then $8h^2$ is equal to (in $ab$)

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