.: Conics: Hiperbola :.

Hiperbola:
Given two points F1 and F2, named loci, and a constant K (K < ||F1-F2||), the hiperbola defined by the triple (F1,F2,k) is the geometric place of the points P that, in absolute value, the difference between the distance P to F1 and the distance P to F2 is exactly k.
Hiperbola={P : | ||P-F1|| - ||P-F2|| | = k}.

Dettails Construction

Construction's details
  1. Define the foci F1 and F2 of the hiperbola, and build a circumference of center F1, containing the point A and leaving the point F2 in its exterior.
  2. Build a "free" point B over the circumference. Build the segment BF2 and the midpoint C of this segment.
  3. Build the line r, perpendicular to the segment BF2 passing by C (this line will be the bisector of BF2). Then build the line s passing by F1 and by B.
  4. Define the point D as the intersection between the lines r and s.
  5. Trace the point D: move the point B over the circumference and observe the "locus" defined by the point D.

Interactive construction

Below we present the construction proposed above, directly on iGeom.
Note that some auxiliary objects to create the hiperbola'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 hiperbola (F1, F2 or R) to see what happens with the hiperbola. One can also move the point A over the circumference C0, it is the point that generates the "locus" (from the point P, in this case it will be possible to observe that this point "walks through" the hiperbola).

To move a point, the button "move" must be selected .