Rectangle $ABCD$ has area 200.An ellipse with area $200\pi$ passes through $A$ and $C$ and has foci at $B$ and $D$.Find the perimeter of the rectangle.
Let the side lengths of the rectangle ABCD be $l$ and $\frac{200}{l}$ and the foci of the rectangle be $(-c,0)$ and $(c,0)$
So $2c=\sqrt{l^2+\frac{40000}{l^2}}$
$4c^2=l^2+\frac{40000}{l^2}$
And the area of the ellipse is $200\pi=\pi ab$
where the $a$ and $b$ are the semi major axes and semi minor axes of the ellipse.
I cannot complete the solution.I am confused where to take the origin and what are the coordinates of $A$ and $C.$