Question

Find the dimensions of the largest rectangle with sides parallel to the axes that can be inscribed in the x^2+4y^2=4 as shown in below.

Answer 1

HI!!

Answer 2

guess this is a nice ellipse right?

Answer 3

The AREA of such a rectangle would be \(4\cdot x_{0}\cdot y_{0}\), just working in the first quadrant.

Answer 4

a point in the first quadrant will look like
\[(x,\frac{\sqrt{4-x^2}}{2})\]

Answer 5

the area of that part will be
\[A(x)=\frac{x\sqrt{4-x^2}}{2}\] maximize that one

Answer 6

:)

Answer 7

here is a trick!

Answer 8

u know a square would be the biggest area inscribed in a circle so if we were to rescale the y axis or xaxis

Answer 9

@dan815 it is "inscribed" right?

Answer 10

yes im just using the guidelines to draw a nice ellipse