Ever wondered what does it mean that a parabola is tangent to the line of infinity, or that a hyperbola cuts it twice?

```
# Parabola - tangent to the line of infinity
p = x^2-y
# Hyperbola - cuts twice the line of infinity
p = x^2-y^2+16
# Singular Cubic - has a point of inflection tangent to the line of infinity
p = x^2+x^3/2-y^2
```