Find the lines through the point (0,2) making angles `pi/3` and`(2pi)/3` with the x-axis. Also, find the lines parallel to the cutting the y-axis at a distance of 2 units below the origin.

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

Find the equation of the line through the point (0, 2) making an angle pi/6 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.

Find equation of the line passing through point (0,3) and making an angle (2pi)/(3) with the positive x-axis. Also, find the equation of the line perllel to it and crossing the y axis at a distance of 3 units below the origin.

Find the equation of the line through the point (1, -2) making an angle of 135^(@) with the x-axis.

Write down the equation of the following lines: A line parallel to x-axis at a distance of 3 units below x-axis.

Find the equation of a straight line: with slope -2 and intersecting the x-axis at a distance of 3 units to the left of origin.

Find the equation of the lines through the point (3, 2) which make an angle of 45 with the line x-2y=3 .

Find the equation of the line parallel to the y-axis and 3 units to the right of it.

Find the equation of the line through the point A(2,3) and making an angle an angle of 45^0 with the x-a xi s . Also, determine the length of intercept on it between A a n d the line x+y+1=0.

If the straight line drawn through the point P(sqrt3,2) and making an angle (pi)/(6) with the x-axis meets the line sqrt3x-4y+8=0 at Q, find the length of PQ.