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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