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 30° with positive direction of the x-axis.

Asked by Pragya Singh | 11 months ago |  87

Solution :-

Given: θ = 30°

We know that slope, m = tan θ

m = tan30° = ($$\dfrac{1}{\sqrt{3}}$$)

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

So, y = $$\dfrac{1}{\sqrt{3}}x$$ + 2

y = $$\dfrac{x+2\sqrt{3}}{\sqrt{3}}$$

$$\sqrt{3}y= x +$$  $$2 \sqrt{3}$$

$$x- \sqrt{3}y+ 2 \sqrt{3}=0$$  

The equation of the line is

$$x- \sqrt{3}y+ 2 \sqrt{3}=0$$

Answered by Abhisek | 11 months ago

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