Point-Point
This activity belongs to the GeoGebra book GeoGebra Principia.
When the sum of the distances from the points of the sought-after locus to points A and B is constant, we obtain an ellipse.
When the difference of the distances from the points of the sought-after locus to points A and B is constant, we obtain a branch of a hyperbola. (In the case where the constant is 0, we obtain the perpendicular bisector.)
When the product of the distances from the points of the sought-after locus to points A and B is constant, we obtain a Cassini oval 
. If the constant coincides with the square of half the distance AB, we obtain a Bernoulli lemniscate .
Surprisingly , , when the quotient of the distances from the points of the sought-after locus to points A and B is constant, we obtain a circle. (In the case where the constant is 1, we obtain the perpendicular bisector.)
. If the constant coincides with the square of half the distance AB, we obtain a Bernoulli lemniscate .
Surprisingly , , when the quotient of the distances from the points of the sought-after locus to points A and B is constant, we obtain a circle. (In the case where the constant is 1, we obtain the perpendicular bisector.)
- Note: For a better view of the construction, it is recommended to download the ggb file here.
Author of the construction of GeoGebra: Rafael Losada.