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Question -

Find the equation of the line on which the 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°.



Answer -

Given:

p = 4, α = 30°

The equation of theline in normal form is given by

Using the formula,

x cos α + y sin α= p

Now, substitute thevalues, we get

x cos 30° + y sin 30°= 4

x√3/2 + y1/2 = 4

√3x + y = 8

The equation of linein normal form is √3x + y = 8.

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