# The straight line L at a distance of 4 units from the origin makespositive intercepts on the coordinate axes and the perpendicularfrom 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) $(\sqrt3-1)x+(\sqrt3+1)y=8\sqrt2$

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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