# An ellipse

- Author:
- Zoltán Kovács

- Topic:
- 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.