a line is drawn through the point P(2,3) and is inclined at an angle of 30o with the X-axis. find the equation of the line and co-ordinates of two points on it at a distance of 6 units from P on either side of P.
It is given that x1 = 2, y1 = 3
We know that, slope of line (m) = tanθ
∴ m = tan 30°
So, the equation of the line is given by,
This is the required equation of the line.
Now, suppose that (x2, y2) be any point on line (1). So it will satisfy equation (1).
And (x2, y2) is at a distance of 6 units from P (2, 3).
∴ By distance formula,
∴ From (2), we have
Hence, the co-ordinates of two points on the line are .