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

re: General Solution by ThoughtProvoker)

After giving it some additional thought, I have an answer to my question.

Brian, I think had it as an underlying assumption, or at least didn't
address it. Basically, if we assume there is a smaller
circumscribing ellipse in the original space, then because of the
consistency of ratios of area (between transformations), that smaller
ellipse would have a corresponding ellipse (circle) in the transformed
space. This leads to a contradiction, so the assumption is
invalid.

I like it. And Richard has a nice point about answering *only* the question asked, but I also appreciate the extra detail Brian gave.

Kudos to both of you.