# Reduce the equation x – √3 y + 8 = 0 into normal form. Find their perpendicular distances from the origin and angle between perpendicular and the positive x-axis.

Equation of line in normal form is given by x cos θ + y sin θ = p where ‘θ’ is the angle between perpendicular and positive x axis and ‘p’ is perpendicular distance from origin.

Given equation is x – y + 8 = 0

Dividing both sides by

The above equation is of the form x cos θ + y sin θ = p, where θ = 120° and p = 4.

Perpendicular distance of line from origin = 4

Angle between perpendicular and positive x – axis = 120°

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