Parabola - Geometric Definition I

Draw a dynamic geometric figure illustrating the geometric definition of a parabola: the locus of points equidistant from a fixed point (focus) and a fixed line (directrix). Start with a horizontal line as the directrix and a fixed point above it as the focus. Draw a circle centered at the focus with a variable radius, intersecting the directrix at two points and also intersecting a vertical auxiliary line through the focus at two other points. From each intersection on the directrix, draw a perpendicular segment to the directrix, and mark the angle between this segment and the line connecting the focus to the foot of the perpendicular. As the radius varies, the traced paths of these intersection points form two symmetric curve branches, and finally a complete parabola is fitted through five traced points. The figure should clearly show the focus, directrix, perpendicular segments, and angle markers to visualize the equal-distance condition.