Consider a line AB makes an angle with the positive direction of x – axis and a point on the line is .

Let a general point P on the line AB and the distance between P and Q is r._{}

Draw a line QL, PM perpendicular to x-axis and draw.

In a right angled triangle PQN,

Therefore,

Therefore, the equation of a straight line in parametric form is:

__Example:__

**Determine the equation of a line passes through the point (–1, – 2) and makes an angle of 30^{o }with the positive direction of x-axis, in parametric form. Find the coordinates of a point at distance of 2 units.**

The equation of the line is:

The coordinates of the point are.

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