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how to determine the center or foci of an ellipse from a slope


Hi guys,
I have a slope field (2d-array), which is defined
by ellipses (can be arbitrarily tilted), which all have the 
same foci and center but different major and minor half axes. 
In fact, I obtained the tangent at each point by measurements.

Does somebody have an idea on how to approach the problem 
of finding the center or the foci of the ellipses? I think 
there is no exact solution to the problem?

Best Regards,
Thomas


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