Dear Bernard

> THEY DO, dear Jean-Pierre !

Of course, you're right - in fact I was thinking to your points UVW -

Looking at your nice page about Darboux, I have an obvious explanation

of the nice property of the pedal triangle of U,V,W.

Suppose that A'B'C' is the pedal triangle of M; then BB' and CC' are

parallel iff M lies on your hyperbola Ha.

As U,V,W are the common points of Ha,Hb,Hc, for these points, AA',

BB', CC' are parallel.

Thus, there is nothing new in what I said.

Friendly.Jean-Pierre