A Point and a Circle
This activity belongs to the GeoGebra book GeoGebra Principia.
If the point is inside the circle, we obtain an ellipse, and if it's outside, a branch of a hyperbola.
The implicit curve of the ellipse or branch of the hyperbola is given by the equation:
XA – Xc = 0
Note that a construction similar to the one for the parabola also allows us to generate this locus.
Author of the construction of GeoGebra: Rafael Losada.