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(Geogebra exercise) Illustrate the following statement: Tangents drawn to two confocal parabolas from a point on the common tangent intersect at the same angle as the axes of the parabolas.
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Solution:
I first constructed a slider for a. Then I created the focus point (a,0) and point A(-a,0). Then I created a slider for m and line y=m(x+a)-line f. I created the perpendicular bisector (line g) to A and then focus point. Then, I created a slider for m_2. Then, created the line y=m_2(x+a)- line h. I created parabolas with the focus point and directrix line h and then line f. I created point P on line g. Then, I created the tangent point from the parabola to point P. I constructed a point on line l and I and then the angle CPB. I constructed a perpendicular line to lines f and h through the focus point (lines n and p). I created the intersection points on p and n.