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

1 Answer

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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