An ellipse
LocusEquation[a+b==3c/2,C] asks GeoGebra to show the possible set of points of C with the given condition. This condition defines an ellipse.Activity
Create a similar triangle and try to play with the setting 3c/2. This constant is actually (3/2) times c. What happens if you change the number 3/2 a different one?
An issue
Even if it is geometrically impossible, GeoGebra will plot a curve for
LocusEquation[a+b==c/2]. Indeed, a+b should always be greater than c due to the triangle inequality.
What happens here? Actually, GeoGebra cannot distinguish between the + (plus) and - (minus) operations here, because of the limitations of the underlying theory, namely complex algebraic geometry. So actually it computes LocusEquation[a-b==c/2] which yields indeed a hyperbola.
One should keep in mind that the output of the LocusEquation command is always a possible superset of the real geometrical output.