How to find a point on an hyperbola from a nearby point?

Working on FreeCAD. In the sketcher I'm making the snapping feature for hyperbolas curves.

There is an hyperbola, the user put the mouse pointer close to it (point A). So A is close to the hyperbola, but not exactly on it. I need to calculate the coordinates of the point B which is on the hyperbola. (then the point B is used to override A (mouse coordinates), such that the hyperbola is exactly under the mouse pointer).

On OCC doc I found the formula :

B = centerPoint + majorAxis * cosh(U) + minorAxis * sinh(U);

Which works as it calculate points on the hyperbola. However I can't find how to calculate U (ie the parameter). I have centerPoint, MajorAxis, MinorAxis and can access the OCC library.

Anyone knows how to find B or U?
Thanks!

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