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Help me understand! - Co-ordinate geometry - JEE Main-7

The straight line L at a distance of 4 units from the origin makes

positive intercepts on the coordinate axes and the perpendicular

from the origin to this line makes an angle of 60^{\circ} with the line 

x+y=0 . Then an equation of the line L is :

  • Option 1)

    x+\sqrt3y=8

  • Option 2)

    (\sqrt3+1)x+(\sqrt3-1)y=8\sqrt2

  • Option 3)

    \sqrt3x+y=8

  • Option 4)

    (\sqrt3-1)x+(\sqrt3+1)y=8\sqrt2

 
Answers (1)
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Hence, the equation of line is 

xcos\theta+ysin\theta=p

xcos75^{\circ}+ysin75^{\circ}=4

x(\frac{\sqrt3-1}{2\sqrt2})+y(\frac{\sqrt3+1}{2\sqrt2})=4

(\sqrt3+1)x+(\sqrt3-1)y=8\sqrt2


Option 1)

x+\sqrt3y=8

Option 2)

(\sqrt3+1)x+(\sqrt3-1)y=8\sqrt2

Option 3)

\sqrt3x+y=8

Option 4)

(\sqrt3-1)x+(\sqrt3+1)y=8\sqrt2

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