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(B) Let the slopes of the lines be $m_1 = 	an \alpha$ and $m_2 = 	an \beta$.The equation $ax^2 + 2hxy + by^2 = 0$ represents two lines passing throu

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$\frac{2h}{a - b}$

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(B) Let the slopes of the lines be $m_1 = 	an \alpha$ and $m_2 = 	an \beta$.The equation $ax^2 + 2hxy + by^2 = 0$ represents two lines passing through the origin.From the properties of quadratic equations in homogeneous form, the sum of the slopes is $m_1 + m_2 = -\frac{2h}{b}$ and the product of the slopes is $m_1 m_2 = \frac{a}{b}$.Using the trigonometric identity for the tangent of a sum: $	an(\alpha + \beta) = \frac{	an \alpha + 	an \beta}{1 - 	an \alpha 	an \beta}$.Substituting the values: $	an(\alpha + \beta) = \frac{m_1 + m_2}{1 - m_1 m_2} = \frac{-\frac{2h}{b}}{1 - \frac{a}{b}}$.Simplifying the expression: $	an(\alpha + \beta) = \frac{-\frac{2h}{b}}{\frac{b - a}{b}} = \frac{-2h}{b - a} = \frac{2h}{a - b}$.

If the angles made by the lines represented by the equation $ax^2 + 2hxy + by^2 = 0$ with the $X$-axis are $\alpha$ and $\beta$, then $\tan(\alpha + \beta)$ is

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