The joint equation of the pair of lines passi | vedclass

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(B) Let the two lines passing through the origin be $L_1$ and $L_2$. Since they form an equilateral triangle with the line $y=3$,the angle made by the

Vedclass · Accepted Answer

$3x^2-y^2=0$

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(B) Let the two lines passing through the origin be $L_1$ and $L_2$. Since they form an equilateral triangle with the line $y=3$,the angle made by these lines with the $x$-axis must be $60^{\circ}$ and $120^{\circ}$.The slopes of these lines are $m_1 = 	an(60^{\circ}) = \sqrt{3}$ and $m_2 = 	an(120^{\circ}) = -\sqrt{3}$.The equations of the lines are $y = \sqrt{3}x$ and $y = -\sqrt{3}x$.Rearranging these,we get $\sqrt{3}x - y = 0$ and $\sqrt{3}x + y = 0$.The joint equation is given by $(\sqrt{3}x - y)(\sqrt{3}x + y) = 0$.Expanding this,we get $(\sqrt{3}x)^2 - y^2 = 0$,which simplifies to $3x^2 - y^2 = 0$.

The joint equation of the pair of lines passing through the origin and forming an equilateral triangle with the line $y=3$ is

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