Optimization: Find the largest possible rectangle inscribed in an ellipse

Optimization: Find the largest possible rectangle inscribed in an ellipse

[lukeeeee]

I watched 3 videos before this that had many views and I still did not understand... watched this partly and understood it in it's entirety

[ibrahimismael]

Thank You for explanation .. can you solve the same question for the ellipse || x^2/16 + y^2/25 = 1 || my my solution was = 40π cm^2

[Bangalibabu]

Can't we assume different value in place of x and y ?
Will it give different result? Like if we assume (x/2, y/2) in place of (x, y).

[lukeeeee]

lol it is always the square root of half the denominator