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Question
Find the equation of the line where length of the perpendicular segment from the origin to the line is 4 and the inclination of the perpendicular segment with the positive direction of x-axis is 30°.
Solution
The normal form of the equation of the line is x cos ω + y sin ω = p.
Here p = 4 and ω = 30°.
Therefore, the equation of the line is x cos 30° + y sin 30° = 4
`x sqrt(3)/2+ y 1/2` = 4
or `sqrt(3) x + y` = 8
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