[code]LocusEquation[a+b==3c/2,C][/code] asks GeoGebra to show the possible set of points of [i]C[/i] with the given condition. This condition defines an ellipse.
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?
Even if it is geometrically impossible, GeoGebra will plot a curve for [code]LocusEquation[a+b==c/2][/code]. Indeed, [i]a[/i]+[i]b[/i] should always be greater than [i]c[/i] due to the triangle inequality.[br][br]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 [code]LocusEquation[a-b==c/2][/code] which yields indeed a hyperbola.[br][br]One should keep in mind that the output of the [b]LocusEquation[/b] command is always a possible superset of the real geometrical output.