I'm looking for a software tool to plot live contour plots.
With live I mean something like Desmos, where you can enter formulas with parameters, and then adjust the parameters interactively (with a slider).
With coutour plot I mean something like this:
You can probably do it easily in Mathematica and turn it into an interactive demonstration that can be played with the free CDF player.
For examples, see the Wolfram Demonstrations Project, which includes source code for many examples. The example below should get you started:
These pages should help you get started with CDF:
Getting Started with the Computable Document Format (CDF)
Create a Computable Document Format (CDF) File