What is the area of the smallest ellipse that can be circumscribed around a 3-4-5 triangle?

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What is the area of the largest ellipse that can be inscribed in a 3-4-5 triangle?

(In reply to

circumscribe sol w just 1st calculus by vectorboy)

There is only one problem with your solution, it assumes the axes of the ellipse are parallel to the legs of the triangle. That is not true for the absolute minimal ellipse.