Parametric Equations

(Select the images below for Desmos pages).
These can be entered in a similar way to coordinates, you can then edit the domain.

The sliders feature can be used too, for example try this graph of a circle given in terms of its parametric equations. Selecting the slider allows editing, for example as here it is possible to set the interval so that only integer values are possible.

Select image to see graph page

Now, to get more sophisticated – I wanted to show students how a parametric curve related to the values of the parameter – so created this very simple graph page.
Selecting the symbols on the left  means you can display / hide parts of the graph. (My defense of simple is that I’m showing students syntax they can easily cope with).

However, what I really wanted  was to be able to use sliders within the domain as I had for polar curves. Not sure of how to do this, I asked @Desmos on Twitter – their reply:

Oh yes! Look at the fabulous graph page from Desmos

Select image to see this in action!