Posted by **Micah** on Sunday, July 11, 2010 at 10:45pm.

What is the largest rectangle that can be inscribed in the first quadrant of the ellipse 9x^2+16y^2=144?

- Calculus -
**Reiny**, Monday, July 12, 2010 at 7:09am
base along x-axis, height along y-axis, bottom left vertex at (0,0).

let the top right vertex be (x,y)

from equation

y = (1/4)√(144 - 9x^2)

Area = xy

= x(1/4)√(144 - 9x^2)

differentiate using the product rule, set the derivative equal to zero and solve for x

I got x = 4√3/3 for a max area of 384√3/3

but check my arithmetic.

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