Perpendicular distance from the origin is 5 units and the angle made by the perpendicular with the positive x-axis is 30°

Solution:

If p is the length of the normal from the origin to a line and w is the angle made by the normal with the positive direction of the x-axis, then the equation of the line given by

x cos ω + y sin ω = p

Here, p = 5 units and ω = 30°

Thus, the required equation of the given line is

x cos 30° + y sin 30° = 5

x. √3/2 + y. 1/2 = 5

√3x + y = 10

Hence, the equation of the line is √3x + y = 10

NCERT Solutions Class 11 Maths Chapter 10 Exercise 10.2 Question 8

Perpendicular distance from the origin is 5 units and the angle made by the perpendicular with the positive x-axis is 30°

Summary:

The equation of the line whose perpendicular distance from the origin is 5 units and the angle made by the perpendicular with the positive x-axis is 30° is √3x + y = 10.