Envelope of a family of unit circles centered on a parabola
construction of the envelope
The parabola P is given by equation x=y^2.
Consider the family of unit circles centered on P.
Move the center A of the circles. Do you "see" the envelope?
Do you "see" the two components?
Do you identify the cusps of one component of the envelope?
By the same way you can build envelopes of other families of plane curves.