p = 4, α = 150°

Given:

p = 4, α = 150°

The equation of the line in normal form is given by

Using the formula,

x cos α + y sin α = p

Now, substitute the values, we get

x cos 150° + y sin 150° = 4

cos (180° – θ) = – cos θ , sin (180° – θ) = sin θ

x cos(180° – 30°) + y sin(180° – 30°) = 4

– x cos 30° + y sin 30° = 4

\( \dfrac{-\sqrt{3}x}{2}+\dfrac{y}{2}=4\)

\( -\sqrt{3}x + y = 8\)

The equation of line in normal form is \( -\sqrt{3}x + y = 8\)

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