Find the equation of the line on which the length of the perpendicular

1.	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 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 30° + y sin 30° = 4 x√3/2 + y1/2 = 4 √3x + y = 8 ∴ The equation of line in normal form is √3x + y = 8.

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 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 30° + y sin 30° = 4

x√3/2 + y1/2 = 4
√3x + y = 8

∴ The equation of line in normal form is √3x + y = 8.