Curves

GeoGebra supports the following types of curves:

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.

  • 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 Mode point.svg Point or command Point. Since the endpoints a and b are dynamic you can use slider variables as well (see tool Mode slider.svg 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.

Polar curves

In order to draw a curve defined using polar coordinates, it is possible to use one of the following (equivalent) syntaxes:

ρ=sin(2 θ), or sin(2 θ), or f(t)=(sin(2*t); t), or (sin(2*t); t), or f(t)=(sin(2*t); t), 0< t < pi, or (sin(2*t); t), 0 < t < pi, or Curve[(sin(2*t); t), t, 0, 2pi].

Implicit curves

Implicit curves are polynomials in variables x and y. The can be entered directly using the Input Bar. The ImplicitCurve command generates an implicit curve through a list of points.

x^4 + y^3 = 2xy