Tracing a Parabola, from Focus and Directrix

If the animation does not appear, click here.

This animation shows how to trace out a parabola using the focus-directrix definition. (See notes below.)


Given a straight line L (the directrix), a point F (a focus) not lying on that line, the corresponding parabola is the set of all points P for which the distances PF and PL are equal.

In this animation, the vertical line at the left side of the frame is the directrix and the black point to its right is the focus. The blue segment which connects the moving point on the curve to the focus is always the same length as the other blue segment—which is the perpendicular from the moving point to the directrix; this is evident from the circle having both segments as radii.

In this animation, we have placed the directrix just one unit to the left of the focus. (10/30/09)