Find equation of the line through the point (0, 2) making an angle $\frac{2 π}{3}$ with the positive x - axis. Also, find the equation of line parallel to it and crossing the y - axis at a distance of 2 units below the origin.

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Solution

Here $m = t a n \frac{2 π}{3} = t a n 120^{\circ}$

$= t a n (90^{\circ} + 30^{\circ}) = - c o t 30^{\circ} = - \sqrt{3}$

Equation of the line passing through point (0, 2) having slope $- \sqrt{3}$ is

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

Now the line paralled to this line having slope $- \sqrt{3}$ .

Here c = -2.

Putting these values in y = mx + c, we have

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

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Find equation of the line through the point (0, 2) making an angle 2π3 with the positive x - axis. Also, find the equation of line parallel to it and crossing the y - axis at a distance of 2 units below the origin.

Find equation of the line through the point (0, 2) making an angle $\frac{2 π}{3}$ with the positive x - axis. Also, find the equation of line parallel to it and crossing the y - axis at a distance of 2 units below the origin.