Parametric curves

This applet plots and traces a parametric curve, given as a vector function in $\mathbb{R}^2$.

Enter the $\bf i$ and $\bf j$ components of your vector function in the textboxes, or choose an example from the dropdown menu. Drag the slider for $t$ to trace out the path ${\bf{r}}(t)$, or click ‘Animate’ to trace out the path automatically.

What shape does the point ${\bf{r}}(t)$ trace out as t changes? Click ‘Show parametric curve’ to see the entire parametric curve.

You can add in the velocity $\bf v$ and acceleration $\bf a$ vectors using the checkboxes.

The ‘Show i,j curves’ checkbox shows the $\bf j$-component as a function of $t$ along the horizontal axis, and the $\bf i$-component as a function of $t$ along the vertical axis.

Other resources:

Geogebratube page for this applet

Two parametric curves applet