algebraic curves

Circle:
[[-1,0,1],[0,0,0],[1,0,0]]
[-2,2]
[-2,2]

Ellipse:
[[-1,0,1],[0,0,0],[2,0,0]]
[-2,2]
[-1,1]

Cross:
[[0,0],[0,1]]
[-1,2]
[-2,1]

Parabola:
[[0,-1],[0,0],[1,0]
[-1,3]
[-2,2]

EllipticCurve:
[[-1,1,0,-1],[0,0,0,0],[1,0,0,0]]
[-2,2]
[-3,3]

FoliumofDescartes:
[[0,0,0,1],[0,-3,0,0],[0,0,0,0],[1,0,0,0]]
[-3,3]
[-3,3]

Lemniscate:
[[0,0,-1,0,1],[0,0,0,0,0],[1,0,0,0,0]]
[-2,2]
[-1,1]

Trifolium:
[[0,0,0,-1,1],[0,0,0,0,0],[0,3,2,0,0],[0,0,0,0,0],[1,0,0,0,0]]
[-1,1]
[-1,1]

Astroid:
[[-1,0,3,0,-3,0,1],[0,0,0,0,0,0,0],[3,0,21,0,3,0,0],[0,0,0,0,0,0,0],[-3,0,3,0,0,0,0],[0,0,0,0,0,0,0],[1,0,0,0,0,0,0]]
[-1,1]
[-1,1]