Find equation of the line through the point (0, 2) making an angle 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

The slope of the line making an anglewith the positive x-axis is

Now, the equation of the line passing through point (0, 2) and having a slope is.

The slope of line parallel to line is.

It is given that the line parallel to linecrosses the y-axis 2 units below the origin i.e., it passes through point (0, –2).

Hence, the equation of the line passing through point (0, –2) and having a slope is

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