Intersecting the y-axis at a distance of 2 units above the origin and makes an angle of 30° with the positive direction of the x-axis

Solution:

It is known that if a line with slope m makes y-intercept c , then the equation of the line is given as y = mx + c.

Here, c = 2 and m = tan 30° = 1/√3

Thus, the required equations of the given line is

y = (1/√3)x + 2

y = (x + 2√3)/√3

√3y = x + 2√3

x - √3y + 2√3 = 0

Hence, the equation of the line is x - √3y + 2√3 = 0

NCERT Solutions Class 11 Maths Chapter 10 Exercise 10.2 Question 6

Intersecting the y-axis at a distance of 2 units above the origin and makes an angle of 30° with the positive direction of the x-axis.

Summary:

The equation of the given line Intersecting the y-axis at a distance of 2 units above the origin and makes an angle of 30° with the positive direction of the x-axis is x - √3y + 2√3 = 0