Find the equation of the line which is at a perpendicular distance of 5 units from the origin and the angle made by the perpendicular with the positive x -axis is 30°
The perpendicular distance of the line from the origin is 5 units and the angle made by the perpendicular with the positive x-axis is 30 ° .
The formula for the equation of line in normal form with p be the length of perpendicular from origin to the line and ω be the angle which the perpendicular makes with positive direction of x-axis is given by,
x cos ω + y sin ω = p (1)
Substitute 5 units for p and 30 ° for ω in equation (1).
x cos 30 ° + y sin 30 ° = 5 x ⋅ 3 2 + y ⋅ 1 2 = 5 3 x + y = 5 × 2 3 x + y = 10
Thus, the equation of line with perpendicular distance from the origin of 5 units and angle of perpendicular 30 ° is 3 x + y = 10 .
The perpendicular distance of the line from the origin is 5 units and the angle made by the perpendicular with the positive x-axis is
The formula for the equation of line in normal form with
Substitute 5 units for
Thus, the equation of line with perpendicular distance from the origin of 5 units and angle of perpendicular
