Ellipse construction

Thank you for the answer, but for some reason this does not work on certain conditions.

For example check this:

https://www.geogebra.org/cl...

This works well if Point F is free-floating.

But then try to set F as Point(g)

The ellipse will suddenly disappear. Is there any way to fix this?

Sorry, in this moment (and with the 5 point approach) I see no possibility for a 100% solution. But try Version 3 (with approximation), this works maybe better.

I see, that's a shame. Maybe it's possible with a different approach?

I tried it, but the problem is the third point isn't free.

Also I just noticed your edit with Version 3, I didn't see it somehow. It seems the problem with the initial version is that if the third point is along a line perpendicular to the centre of the line between point 1 and point 2, the ellipse becomes undefined. But Version 3 seems to fix this problem

But what do you mean by 'approximation'?

aproximativ:

The drawn ellipse does not pass exactly through point C but through point C''. This point is (if necessary) shifted very, very little (much smaller than 1 pixel when standard zoom) in the right angle to direction of the half-axes.

Thus, all values derived from the ellipse (area, perimeter etc) are not entirely accurate but aproximative (small fake but more useful than correctly nothing)

Thank you for your effort. But it seems this method also doesn't work very well when the free point is along the path of the ellipse's minor axis.