# Difference between revisions of "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.

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.

## Polar curves

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

Example: `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.

Example: `x^4 + y^3 = 2xy`
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