Q. 64.4( 58 Votes )

# In Exercises, find the equation of the line which satisfy the given conditions:Intersecting the y-axis at a distance of 2 units above the origin and making an angle of 30o with positive direction of the x-axis.

We know that the point (x, y) on the line with slope m and y-intercept c lies on the line if and only if y = mx + c.

If distance is 2 units above the origin, c = +2

Given θ = 30°

We know that slope, m = tanθ

m = tan30° = (1/3)

y = (1/3)x + 2

y = (x + 23) / 3

3 y = x + 23

x - 3 y + 23 = 0

Ans. The equation of the line is x - √3 y + 2√3 = 0.

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