How to find a parametrization of a equation and to draw its picture.

Question

I was wondering how to find a parametrization of $(x-t)^2+(y-t^2)^2-t^2=0$, and how to use a software like Mathematica to draw a picture of this equation based on the parametrization.

Thanks in advance.

Answer 1

You can use ContourPlot3D. Here is an example parametrization:

ContourPlot3D[(x - t)^2 + (y - t^2)^2 == t^2, {x, -2, 2}, {y, -2, 2}, {t, -1, 1}]