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.

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