Find the equation of the line which is at a perpendicular distance of 5 units from theorigin and the angle made by the perpendicular with the positive x-axis is 30°.

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If p is the length of the normal from the origin to a line and ω is the angle made by the

normal with the positive direction of the x-axis

Then, the equation of the line for the given condition is written by

x cos ω + y sin ω = p.

Here, p = 5 units and ω = 30°

Thus, the required equation of the given line is

x cos 30°+ y sin 30° = 5

x(√3/2) + y(½) = 5

It becomes

√ 3x +y = 10

Thus, the required equation of a line is √ 3x + y = 10

Thanks