Nested focusing parabolas

Doge Dish

All the light coming in from x=4.5 to 10 gets focused to a spot about .1 across.
I figured it out with a great program geogabra.. this is how it looks in the program:

as you slide the slider in the top left from 10 to 4.5 the spot E on the x axis moves very little, over a range of .1.

Now because it can't be revolved around the focal point without self intersecting you would have to do partition the revolution so that alternating pieces around the perimeter are one of these curves then the other.
Then I figure from the area of light reflected to the spot it would reflect on this array has an amplification of around 3000x...