You can drag all the intervals on the bold black line by using the yellow point
on the bold conic, and can drag the green and black lines independently. The
Invariants are the
intersections of the conic and the black line; the Directrices are the
intersections of the conic and the green line.


First, drag the
bold black line clear of the conic, to see the
intervals
on that line freed from restraint (drag the yellow point) as the two invariants go imaginary,then,
drag the bold green line clear of the conic, to see those intervals, and the net that formed them, go imaginary.
Do note that the
nowimaginary net still forms real
conics.

The key insights here are that equivalent or identical intervals are formed on all the conics,
and that the defining black and green lines form the degenerate conic of the set. Thus we have
two perspectivities
in the directrices on the green line participating in a projectivity that
always forms intervals
whatever the state of these invariants  real, or imaginary.
