Given two points F1 and F2, named foci, and a constant K
(K >= ||F1-F2||), the ellipse
defined by the triple (F1,F2,k) is
the geometric place of the points P that the sum of the distances between P and F1
and between P and F2 is exactly k.
Ellipse = {P : ||P-F1|| + ||P-F2|| = k}.
Given two points F1 and F2 in the plane, they will be the foci of the ellipse.
Build a circumference in the center F1, that contains the point A,
in a way that F2 be within.
Build a "free" point B over the circumference, build the segments
BF1 and BF2.
Build the bisector s of BF2 (example, find the midpoint C of the segment
BF2 and build the line s, perpendicular to BF2 in the point C).
Define the point D as the intersection of the line s with BF1 and
build the segment DF2.
Trace the point D: move B and see the "locus" created by the point D.
(or use the option of "locus" of iGeom: select the "free" point B and the point D,
then click the button "locus" and
inside the menu "edit" ).
Interactive construction
Below we present the construction proposed above, directly on iGeom.
Note that some auxiliary objects to create the ellipse's locus are hidden.
To see them,
"click" the button
,
which is inside the primary button
.
If you wish a brief description, in the form of an algorithm, put the pointer over the iGeom's drawing area,
then "click" the mouse's middle button
(if you don't have three buttons, try clicking both simultaneously - eventualy
this emulates the middle button).
Move one of the points that define the ellipse (F1, F2 or R) to see what happens
with the ellipse. One can also move the point A over the circumference C0, is the point that generates the "locus"
(from the point P, in this case it will be possible to see that this point "walks through" the ellipse).
To move a point, the button "move" must be selected
.
and
inside the menu "edit" 
).
,
which is inside the primary button
.