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I want to determine the largest area ellipse inscribed in a rectangle, in order to write a code that can determine the lengths c and d given a and b (see image here). I know the obvious answer would be c and d are halves of a and b, but I want the derivation (and also the maximum area) so I can stop thinking about this, saddly I can't seem to figure this one out. I remember doing the opposite in school (rectangle inside ellipse) but can't do it properly now.

Hope you can help me.

felipe
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    Scale the given rectangle, to make it a square. Clearly the largest ellipse that fits in the square is the incircle of the square. Now scale the square back to the original rectangle, and you have your largest ellipse. –  Oct 11 '23 at 22:03
  • Do you know the formula for the area of an ellipse? How are you planning to vary the ellipse inside the rectangle? – Ted Shifrin Oct 11 '23 at 23:17
  • Please refer to my post concerning Lissajous ellipse here. – Ng Chung Tak Oct 12 '23 at 09:38

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