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Question

(A) The first quadrant is the region between the positive $x$-axis $(0^\circ)$ and the positive $y$-axis $(90^\circ)$.Lines that trisect the first qua

Vedclass · Accepted Answer

$\sqrt{3} x^2 - 4xy + \sqrt{3} y^2 = 0$

Vedclass · Answer

(A) The first quadrant is the region between the positive $x$-axis $(0^\circ)$ and the positive $y$-axis $(90^\circ)$.Lines that trisect the first quadrant make angles of $30^\circ$ and $60^\circ$ with the positive $x$-axis.The equations of these lines are $y = 	an(30^\circ)x$ and $y = 	an(60^\circ)x$.$y = \frac{1}{\sqrt{3}}x \implies x - \sqrt{3}y = 0$$y = \sqrt{3}x \implies \sqrt{3}x - y = 0$The joint equation is $(x - \sqrt{3}y)(\sqrt{3}x - y) = 0$.Expanding this: $\sqrt{3}x^2 - xy - 3xy + \sqrt{3}y^2 = 0$.$\sqrt{3}x^2 - 4xy + \sqrt{3}y^2 = 0$.

The joint equation of the lines passing through the origin and trisecting the first quadrant is

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