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NCERT Class XI Mathematics - Straight Lines - Solutions

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Question : 28 of 74
Marks: +1, -0
Find equation of the line through the point (0, 2) making an angle 2π3\frac{2\pi}{3} with the positive x-axis. Also, find the equation of the line parallel to it and crossing the y-axis at a distance of 2 units below the origin.
Solution:  
Here, m = tan 2π3\frac{2\pi}{3} = - 3\sqrt{3}
The equation of the line passing through point (0, 2) is y − 2 = − 3\sqrt{3} (x - 0)
3x+y2\sqrt{3}x+y-2 = 0
The slope of line parallel to 3x+y2\sqrt{3}x+y-2 = 0 is - 3\sqrt{3}
Since, it passes through (0, –2).
So, the equation of line is 2 y + 2 = − 3\sqrt{3} (x - 0) ⇒ 3x+y+2\sqrt{3}x+y+2 = 0.
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