# Find the equation of the line perpendicular distance from the origin is 5 units and the angle made by the perpendicular with the positive x-axis is 30 degree .

$We\;know\;that,\;If\;p\;is\;the\;length\;of\;the\;normal\;from\;origin\;to\;a\;line\\*and\;w\;is\;the\;angle\;made\;by\;the\;normal\;with\;the\;positive\; direction\;of\\*x-axis\;then\;the\;equation\;of\;the\;line\;is\;given\;by\\* \Rightarrow x\cos w+y\sin w=p\\*Here,\;p=5\;units\;and\;w=30^{\circ}\\* Thus,\;the\;required\;equation\;of\;the\;given\;line\;is\\*x\cos 30^{\circ} +y\sin 30^{\circ}=5\\*\Rightarrow \frac{\sqrt3}{2}x+\frac{1}{2}y=5\\* \Rightarrow \sqrt{3}x+y=10\\*$

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