This script draws

1. hyperbola by apex and two points on one half of the branch (hyper command)
2. rectangular hyperbola by apex, one point on a branch and one point inside hyperbola (rhyper command)
3. parabola by apex, one point on a parabola and one point inside parabola (parab command)

in AutoCAD (tested in AutoCAD 2014) and BricsCAD (tested in BricsCAD 16)

All curves are drawn using splines.

Simply type APPLOAD and select this .lsp file.

I think that there are some other hyperbola.lsp and parabola.lsp files on the internet but haven't found them. So I decided to write my own.