Rectangle $ABCD$ has area $2006.$ An ellipse with area $2006\pi$ passes through $A$ and $C$ and has foci at $B$ and $D$. What is the perimeter of the rectangle?
Take a look at:
https://artofproblemsolving.com/wiki/index.php/2006_AMC_12B_Problems/Problem_21
I think it's the problem you're looking for.
+96 
