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