Geometry
Dynamical Geometry Problem Sheet 2: Parabola
Sketches: Martti E. Pesonen
Problems: ?
Let E be the two dimensional Euclidean plane.
Let us assume points, lines and segments to be familiar, also the notion of
distance assumed to be known.
NOTE! If you are not yet familiar with
1) Move and Animate facilities,
2) resetting the sketch and clearing traces,
you are advised to consult
1. First Sketch: Parabola by definition, fixed focus and line
REVISE !!!
Let F be a point, L a line and
AB a segment in the plane.
A parabola with focus point F and leading line L
is the set of point whose distance from the focus F, and the distance from
the line L are equal to the length of AB.
The following dynamical figure illustrates how the
parabola is built from its definition.
Here the focus point and the leading line are fixed,
but the segment can be changed by mouse.
2. Second Sketch: Parabola by definition, free focus and line
The following illustrates how the
parabola is built from its definition.
Here you can drag the focus, the line (using the two magenta points) and
the segment AB.