Can You Find The Area of Greatest Rectangle in a Ellipse | Maximum Area | Ellipse

Can You Find The Area of Greatest Rectangle in a Ellipse | Maximum Area | Ellipse

Topics Covered :-
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[tontonbeber]

Don't need angles ...
(+/-x, +/-y) corners of rect. so area = (2x).(2y) = 4xy
Equation of ellipse y2 = b2 - x2 b2 / a2
x2y2 = x2 b2 - x4 b2 / a2
let z = x2
max of xy is also max of x2y2
d(x2y2)/d(z) = b2 - 2z . b2/a2 = 0
2z = a2
x2 = a2 / 2
x = a V2/2
and by symmetry of equation we can find y = b V2/2
So max area of rect = (2x)(2y) = 2ab

[icems.a.]

Pensé que lo resolvería con integrales y lo hizo de una manera sencilla.Asombroso !!! Lo felicito 👍

[KM-omhm]

Hint: Don't waste your time by doing this by maxima and minima