How to construct a parabola given its focus and two points on it

Question

I need to construct the guideline/directrix and the axis of symmetry of a parabola.

I’ve been given A its focus and two points B and C going through the parabola.

Could you please point me to the technique on how to do this? Thanks a lot!

Answer 1

Draw two circles, having $B$ and $C$ as centers, and passing through $A$. The directrix of the required parabola is any common tangent to both circles.

Answer 2

Repeat of Aretino's construction, including axes of symmetry.Points $(p,q)$ are vertices of the two parabolas possible with two direct tangent directrices shown.