Given: p = 5 and ω = 30°

We know that the equation of the line having normal distance p from the origin and angle ω which the normal makes with the positive direction of x-axis is given by x cos ω + y sin ω = p.

Substituting the values in the equation, we get

x cos30° + y sin30° = 5

x(\( \dfrac{\sqrt{3}}{2}\)) + y(\( \dfrac{1}{2}\)) = 5

\( \sqrt{3x}\) + y = 5(2) = 10

\( \sqrt{3x}\) + y – 10 = 0

The equation of the line is \( \sqrt{3x}\) + y – 10 = 0.

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