The angle between the lines whose intercepts | vedclass

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(C) The equations of the lines are $\frac{x}{a} - \frac{y}{b} = 1$ and $\frac{x}{b} - \frac{y}{a} = 1$. For the first line,the slope $m_1 = \frac{b}{a

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$	an^{-1} \left( \frac{b^2 - a^2}{2ab} ight)$

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(C) The equations of the lines are $\frac{x}{a} - \frac{y}{b} = 1$ and $\frac{x}{b} - \frac{y}{a} = 1$. For the first line,the slope $m_1 = \frac{b}{a}$. For the second line,the slope $m_2 = \frac{a}{b}$. The angle $	heta$ between the lines is given by $	an 	heta = \left| \frac{m_1 - m_2}{1 + m_1 m_2} ight|$. Substituting the values,$	an 	heta = \left| \frac{\frac{b}{a} - \frac{a}{b}}{1 + (\frac{b}{a})(\frac{a}{b})} ight| = \left| \frac{\frac{b^2 - a^2}{ab}}{1 + 1} ight| = \left| \frac{b^2 - a^2}{2ab} ight|$. Thus,$	heta = 	an^{-1} \left( \left| \frac{b^2 - a^2}{2ab} ight| ight)$.

The angle between the lines whose intercepts on the axes are $a, -b$ and $b, -a$ respectively is .....

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