[color=#999999]This activity belongs to the [i]GeoGebra book[/i] [url=https://www.geogebra.org/m/sw2cat9w]GeoGebra Principia[/url].[/color][br][br][br][color=#CC3300][b]The Field of Equidistant Parabolas from a Fixed Line and a Free Point on a Perpendicular Line[/b][/color][br][br]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.[br][br]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. [br][br]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

[color=#999999]Author of the construction of GeoGebra: [url=https://www.geogebra.org/u/rafael]Rafael Losada[/url].[/color]