A line forms a triangle of area $$543$$ $$sq-units$$ with the coordinate axes. If the perpendicular drawn from the origin to the line makes an angle of $$60$$° with the $$x-axis$$, then the equation the line is

Question

A line forms a triangle of area $$543$$ $$sq-units$$ with the coordinate axes. If the perpendicular drawn from the origin to the line makes an angle of $$60$$° with the $$x-axis$$, then the equation the line is

Infinity Learn · Accepted Answer

Let p be the length of the perpendicular drawn from the origin to the required line. The perpendicular makes an angle of $$60$$° with the $$x-axis$$. Putting $$a=$$ $$60$$° in xcos⁡α$$+ysin$$⁡α$$=p$$ the equation of the line is xcos⁡$$60$$∘$$+ysin$$⁡$$60$$∘$$=por$$, $$x+3y=2p$$.This cuts the coordinate axes at $$A(2p$$,$$0)$$ and $$B0$$,$$2p3It$$ is given that           Area of △$$OAB=543$$ sq. units.⇒ $$12(OA)(OB)=543$$⇒ $$12$$×$$2p$$×$$2p3=543$$⇒$$p2=81$$⇒$$p=9Hence$$, the equation of the line is $$x+3y=18$$

A line forms a triangle of area $54 \sqrt{3}$ sq-units with the coordinate axes. If the perpendicular drawn from the origin to the line makes an angle of $60 °$ with the $x -$ axis, then the equation the line is

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A line forms a triangle of area 543 sq-units with the coordinate axes. If the perpendicular drawn from the origin to the line makes an angle of 60° with the x-axis, then the equation the line is

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A line forms a triangle of area $54 \sqrt{3}$ sq-units with the coordinate axes. If the perpendicular drawn from the origin to the line makes an angle of $60 °$ with the $x -$ axis, then the equation the line is