In message , Timothy Murphy
writes
I'm not really clear on this.
I thought that the whole point of using a parabolic surface
was that the (almost) parallel rays from the satellite
would all be reflected to pass through the focus,
and for that I would have thought that
the directrix of the parabola _would_ have to pass through the satellite.

Yes, but if you move the (let's call them parallel) rays off centre,
then the focal point reflected also moves off centre in the other
direction

--
geoff