A Cardioid from a Family of Parabolas
Suppose you are given two distinct points in the plane, A and F. Draw a parabola that passes through A and has F as its focal point. Suppose B is the vertex of this parabola. There are infinitely many such parabolas. The set of all possible locations for B is a cardioid.
In the applet below, A and F are fixed, and you can obtain different parabolas by moving the vertex B.