Parabolas from a Line
This activity belongs to the GeoGebra book GeoGebra Principia.
The Field of Equidistant Parabolas from a Fixed Line and a Free Point on a Perpendicular Line
Let r be the line passing through the fixed points O and I. Let d be the line perpendicular to r at point O, and let A be a point on the line r. We will call dA the parabola of focus A and directrix d.
Now, it's sufficient to extend all the operations already seen between two points A and B to the corresponding ones between the parabolas dA and dB.
If we align the coordinate origin with O and point (1, 0) with I, the point P will correspond to (p, 0), allowing us to represent the parabola dP with the equation: y² = 2p x − p²
Author of the construction of GeoGebra: Rafael Losada.