Since the director circle of a parabola is the directrix itself, does it mean that it has a set of infinite director circles (point circles )?

Question

Here is the result I obtained

The director circle for a parabola is x+a=0 . Where the equation of parabola is taken as y^2=4ax .

Answer 1

No, you consider a straight line as the limit of a circle for $r->\infty$ so you have only one director "circle" Also if you take an ellipse with on axes fixed, the other growing larger and larger the director circle grows and finally it becomes a straight line