The joint equation of two lines passing throu | vedclass

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Question

(C) The lines pass through the origin and make an angle of $30^{\circ}$ with the positive $Y$-axis. The angle made by these lines with the positive $X

Vedclass · Accepted Answer

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

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(C) The lines pass through the origin and make an angle of $30^{\circ}$ with the positive $Y$-axis. The angle made by these lines with the positive $X$-axis is $90^{\circ} \pm 30^{\circ}$,which gives angles of $60^{\circ}$ 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 $y = -\sqrt{3}x$,which can be written as $y - \sqrt{3}x = 0$ and $y + \sqrt{3}x = 0$. The joint equation is $(y - \sqrt{3}x)(y + \sqrt{3}x) = 0$. This simplifies to $y^2 - 3x^2 = 0$,or $3x^2 - y^2 = 0$.

The joint equation of two lines passing through the origin,each making an angle of $30^{\circ}$ with the positive $Y$-axis,is

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