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Question
Find equation of the line through the point (0, 2) making an angle `(2pi)/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
Let a line PQ pass through the point P(0, 2) and make an angle of `(2π)/3` with the positive x-axis.
∴ Slope of PQ = tan `(2π)/3`
= `-sqrt3`
∴ Equation of line PQ, y – y1 = m(x – x1)
y – 2 = `-sqrt3(x – 0)`
or `sqrt3 x + y - 2 = 0`
The second line RS is parallel to line PQ
∴ Slope of RS = `-sqrt3`
This line passes through (0, 2).
Equation of line RS, y – y1 = m(x – x1)
y + 2 = `-sqrt3 (x – 0)`
`sqrt3x + y + 2 = 0`
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