(Geogebra exercise) Illustrate the following statement: Two parabolas have a common focus F; their directrices intersects at a point A. The perpendicular bisector of AF is the common tangent of the two parabolas.
I first constructed the points F(a,0) and A(-a,0). I then created a slider for b. I constructed the line using the equation y=b (x+a). I created the line AF and the perpendicular bisector to it. I constructed the slider for b_2 and the equation y=b_2(x+a). I then constructed the parabolas with focus F and directrix h & f. Then the intersection points of each of the parabolas and the perpendicular bisector.