Tracing a Parabola, from Focus and Directrix
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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)