a line is drawn through the point P(2,3) and is inclined at an angle of 30^{o} 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 *x*_{1} = 2, *y*_{1} = 3

We know that, slope of line (*m)* = tan*θ*

∴ *m* = tan 30°

So, the equation of the line is given by,

This is the required equation of the line.

Now, suppose that (*x*_{2}, *y*_{2}) be any point on line (1). So it will satisfy equation (1).

And (*x*_{2}, *y*_{2}) 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 .

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