SOLUTION: Find the area of the largest possible rectangle that can inscribe in an ellipse. 9x^2 + 4y^2 = 36.

SOLUTION: Find the area of the largest possible rectangle that can inscribe in an ellipse. 9x^2 + 4y^2 = 36.

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Question 1082936: Find the area of the largest possible rectangle that can inscribe in an ellipse. 9x^2 + 4y^2 = 36.

Answer by Fombitz(32388) (Show Source): You can put this solution on YOUR website!
I'll solve the 1/4 problem and then multiply by 4.
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Define a new function which is the square of A,

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Make Z a function of one variable using the ellipse,

Substituting,

Take the derivative of Z with respect to x and set it equal to zero.

is the trivial solution so,

So then solving for ,

So then the maximum area would be,

The width of the rectangle (x direction) would be,

and the length of the rectangle (y direction) would be,

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