The combined equation of a pair of lines pass | vedclass

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(B) The slopes of the lines are $m_1 = 	an(60^{\circ}) = \sqrt{3}$ and $m_2 = 	an(30^{\circ}) = \frac{1}{\sqrt{3}}$.The equations of the lines are $

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$\sqrt{3}(x^2+y^2)=4xy$

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(B) The slopes of the lines are $m_1 = 	an(60^{\circ}) = \sqrt{3}$ and $m_2 = 	an(30^{\circ}) = \frac{1}{\sqrt{3}}$.The equations of the lines are $y = \sqrt{3}x$ and $y = \frac{1}{\sqrt{3}}x$,which can be written as $(\sqrt{3}x - y) = 0$ and $(x - \sqrt{3}y) = 0$.The combined equation is $(\sqrt{3}x - y)(x - \sqrt{3}y) = 0$.Expanding this,we get $\sqrt{3}x^2 - 3xy - xy + \sqrt{3}y^2 = 0$.$\sqrt{3}x^2 - 4xy + \sqrt{3}y^2 = 0$.$\sqrt{3}(x^2 + y^2) = 4xy$.

The combined equation of a pair of lines passing through the origin and inclined at $60^{\circ}$ and $30^{\circ}$ respectively with the $x$-axis is:

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