Conics from a Circle
This activity belongs to the GeoGebra book GeoGebra Principia.
The Field of Equidistant Conics from a Fixed Circle and a Free Point on a Diametral Line
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.
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.
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
Author of the construction of GeoGebra: Rafael Losada.