Constructing limacon and cardiod.

Hit the start button. You have control over the location of point E along the x-axis from 1 TO 4. Point N rotates around point E on a circle of radius 1. The blue circle always contains the origin and is centered at point N. The blue dotted line is tangent to the green circle (that N rotates on). The red dotted line is the perpendicular from the origin to the blue dotted tangent line. The point of intersection of those two lines is traced.