The focus-directrix construction of a parabola
- Author:
- Susan Addington
- Topic:
- Parabola
You can see the steps in the Construction Protocol view. Here they are in English, too.
Construct a point A and a line BC that doesn't contain A.
Construct a point D on BC, not B or C.
Construct the segment AD, then the perpendicular bisector of AD.
Construct the perpendicular to BC at D.
Intersect the last two lines (perpendicular bisector and perpendicular) to get E.
Now form the locus (that is, the trace) of point E as its controller, D, moves along BC:
Choose the Locus tool, at the bottom of the perpendicular set of tools
Click on the point to trace, E, then on its controlling point, D.
A curve appears. As point D moves along BC, point E traces out the curve.
If you change A, B, or C, the shape of the curve changes.
This is a parabola (by definition). It is the set (locus) of points that are equidistant from a point (the focus) and a line (the directrix). Why?
Hints: The perpendicular bisector of a segment is the set of points equidistant from the endpoints of the segment.
How do you measure the distance of a point (E) to a line (BC)?