Hi,
I'm really surprised by the inaccuracy and disappearance of certain conics when zooming in with factors that are not very large/small. I'm talking about zoom factors in the order of 0.01.
In the past I used "Compass and Ruler". (http://en.wikipedia.org/wiki/C.a.R.)
Recently I started using GeoGebra because it has much more to offer.
I tried my examples in "Compass and Ruler" but found no problems there.
Therefore, I think it's a bug in GeoGebra.
I found a remark in the javasource "GeoConicND.java":
/** avoid very large and small coefficients for numerical stability */
protected static final double MAX_COEFFICIENT_SIZE = 100000;
Unfortunately I'm no expert on java so I can't get a quick read from the sources.
Therefore, I give some examples of things that surprise me and I hope that my findings are relevant.
I am using:
GeoGebra 4.4.5.0
Windows 7
Java: Version 7 Update 45 (build 1.7.0_45-b18).
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My first remark is that certain conics don't pass through points which they should do.
I'm giving an example (See attached file and press Zoom-button):
Short description of relevant construction steps.
Create conic through 5 points (Aconic).
Zoomin and see that conic doesn't pass through (0,0).
An intersection from a line with the conic stays in correct place.
A0=(0, 0)
A1=(2, 4)
A2=(6, 4)
A3=(8, 0)
A4=(4,-2)
Aconic=Conic[A0,A1,A2,A3,A4]
SetColor[ Aconic, "Red"]
L=Line[(0, 0.002),(-0.002, 0)]
SetColor[L, "Blue"]
A=Intersect[L, Aconic]
SetActiveView[1]
CenterView[(0,0)]
ZoomOut[0.01/x(Corner[1,3]-Corner[1,1])]
The same problem 
Second remark is that certain conics disappear with Zoomfactor < 0.01.
I'm giving an example (See attached file and press Zoom-button):
Short description of relevant construction steps.
Create a conic through 5 points (Aconic).
Define a Zoomfactor.
Dilate the conic with that zoomfactor (Bconic).
Also Dilate the points with zoomfactor.
Create a conic through the dilated points (Cconic).
The Cconic disappears when Zoomfactor < 0.01.
A0 = (0, 0)
A1 = (2, 4)
A2 = (6, 4)
A3 = (8, 0)
A4 = (4,-2)
Aconic=Conic[A0, A1, A2, A3, A4]
SetColor[ Aconic, "Red"]
ZoomOut=0.008
Bconic=Dilate[Aconic, ZoomOut, A0]
SetColor[ Bconic, "Orange "]
C1 = Dilate[A1, ZoomOut, A0]
C2 = Dilate[A2, ZoomOut, A0]
C3 = Dilate[A3, ZoomOut, A0]
C4 = Dilate[A4, ZoomOut, A0]
Cconic=Conic[A0, C1, C2, C3, C4]
SetColor[ Bconic, "Blue"]
SetActiveView[1]
CenterView[(0,0)]
ZoomOut[ZoomOut / y(Corner[1,3]-Corner[1,1])]
https://ggbm.at/564915
Third remark is that implicit curve disappears.
I'm giving an example (See attached file and press Zoom-buttons):
Short description of relevant construction steps.
Create a conic through 5 points (Pconic).
Define a function like that conic.
Make a Implicit curve for that function (Fconic).
Zoomin and see the disappearance of that implicit curve.
P1 = (0, 0)
P2 = (4,-2)
P3 = (8, 0)
P4 = (6, 4)
P5 = (2, 4)
Pconic=Conic[P1, P2, P3, P4, P5]
SetColor[ Pconic, "Blue"]
f(x,y)=-6x² - 11y² + 48x + 26y
Fconic=ImplicitCurve[f(x, y)]
SetColor[ Fconic, "Red"]
SetActiveView[1]
CenterView[(0.02,0)]
ZoomOut[0.01*10 / y(Corner[1,3]-Corner[1,1])]
https://ggbm.at/564917
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