beginner searching a direction


i want to draw and animate $z^2=a.x^2+(a-1).y^2$ with a travelling from -2 to 3
and plenty of other mathematical curves.
is it possible with Blender or with Python for Blender ?

my aim is to create 3D mathematical shapes that will be printed on a 3D printer

learning Blender is a great amount of work so before to start i would like to have your opinion