Our aim is to obtain a parametric equation using the above presentation. Here is the explanation of the figure given above, a dotted circle shows the previous position of a circle, and O is the initial position of a fixed point . The position of the fixed point is initially at the origin. The circle is rolling towards the negative x-axis. After the circle takes OL units on the line, the new position of the circle is given by the blue circle, and the point P denotes the new position of the point we are tracing.
L is the point of intersection of the later position of the circle and the line.
The point C is the center of the circle. R and K are the legs of the perpendicular segments drawn from P to the segment OL and CL respectively. We are going to find the parametric equation which corresponds to the path. Let's consider the next facts. P after the circle rolled OL units on the line.