Abstract
For an n-by-n matrix A and an elliptic disc E in the plane, we show that the sum of the number of common supporting lines and the number of common intersection points to E and the numerical range W(A) of A should be at least 2n+1 in order to guarantee that E be contained in W(A). This generalizes previous results of Anderson and Thompson. As an application, our result is used to verify a special case of the Poncelet property conjecture.
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