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algebra senior

Problem

A circle of radius passes through both foci of, and exactly four points on, the ellipse with equation The set of all possible values of is an interval What is
(A)
(B)
(C)
(D)
Solution
Note, this is not a full solution but can be used if one is running out of time. As above, the minimum radius of the circle is which is the value. The only answer that contains is
Final answer
D