In this sketch I have values linked to equations used in derived parts. The arc below is fully defined, but I gave it only 3 information (2 points and a radius). The direction of the curvature (convex/concave) is not defined here and I would like to define in an equation. The "focal" variable can take a positive value for a positive curvature and a negative value for a negative curvature.

How can I change my arc direction from my equation parameter?

You could try one of the following indirect things:

I think all of them will be tricky though, as Solidworks is great in figuring out solutions to equations that you didn't anticipate.