It is possible to draw the curve traced out by a point A=(r(t) t). By letting the angle get its value from a slider \(t\), and by defining a function \(r(x)\), When using polar coordinates, a semicolon is used as delimiter, as In GeoGebra you can use polar coordinates when defining a point. Using the tool Locus you can then create the locus by first clicking on \(B\) and then on \(A\) or the slider. The point \(A\) must lie on a curve or a coordinate axis. To make a locus in GeoGebra, you need a point \(B\) that depends either on another point \(A\) or a slider. If you have a point satisfying some condition, then the set of all such points is a locus. In order to use commands for functions, write it as a function, i.e. If a is defined by the equation y=x^2, you cannot use the command If you, for instance, write y = sin(x) GeoGebra will classify this as function, a function that will be given a name by GeoGebra.Īrgument, do not work on conic sections or lines. GeoGebra can create implicit curves defined by equations, if the equations are written using polynomials in \(x\) and \(y\). GeoGebra categorizes a curve defined by an equation as a Line, a Conic, or as an Implicit curve. The curve is implicitly defined by the equation. All points \((x, y)\) satisfying the equation lie on the curve. The equation \(x^2+y^2=1\) defines a curve that is the unit circle. An equation describes a relation between \(x\) and \(y\), and it is not always the case that \(y\) can be expressedĮxplicitly in terms of \(x\). An implicit function is hence a more general concept than a function. An implicit function however, can also have several \(y\)-values corresponding to a \(x\)-value. In this case \(y\) can be expressed explicitly in terms of \(x\) and the curve shown, could also be shown as the graph of the function \(f(x) = x^2\). GeoGebra distinguishes between explicit functions and functions that are defined implicitly by equations in \(x\) and \(y\).Īn explicit function is written by using brackets ‐ using \(f(x)\)-notation.Īn implicit function can be written as \(y=x^2\). Load GeoGebra worksheet Click in the lower left corner to turn off the animation.
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