[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 Conics from a Fixed Circle and a Free Point on a Diametral Line[/b][/color][br][br]Consider a circle with radius s centered at O, and let A be a point on the line r passing through O and I. We will call sA the conic of semiaxis s and foci O (fixed) and A.[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 conics sA and sB. [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 conic sP with the corresponding equation: (2x-p)²/s² − 4y²/(p²-s²) = 1

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