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Homework Statement
Largest possible area of a rectangle inscribed in the ellipse (x2/a2)+(y2/b2)=1
Homework Equations
Area of the rectangle = length*height
The Attempt at a Solution
I have it set up so that the four corners of the rectangle are at (x,y) (-x,y) (-x,-y) (x,-y) and that area therefore is A=(2x)(2y).
In order to find the max area, I know I need to differentiate the equation, so I need to eliminate either x or y.
Using the ellipse equation, I found x to be equal to sqrt(a2-(y2a2)/b2).
Substituting that into the area equation I get:
A=2(sqrt(a2-(y2a2)/b2))*(2y).
And differentiating that has been a nightmare and I haven't gotten it right yet. I know a and b are constants, and become one in the derivative.
But is there any easier way of solving this problem?