Curves

There are two types of curves in GeoGebra:

Parametric curves

Parametric curves of the form a(t) = (f(t), g(t)) where t is real parameter within a certain range can be created:

• using the Curve Command or
• by typing their expression directly in the input bar, e.g.(t^2,t^3).
  

Parametric curves can be used as arguments in the following commands: Tangent, Point, Intersect, Derivative, Length, Curvature, CurvatureVector and OsculatingCircle.

Note:

• Parametric curves can be used with pre-defined functions and arithmetic operations. For example, input c(3) returns the point at parameter position 3 on curve c.
• You can also place a point on a curve using tool Point or command Point. Since the endpoints a and b are dynamic you can use slider variables as well (see tool Slider).

Creating a parametric curve through some given points is not possible. You can however try e.g. FitPoly Command to get a function going through these points.

Implicit curves

Implicit curves are polynomials in variables x and y. The can be entered directly using the Input Bar.

Example: x^4 + y^3 = 2x*y