Hello, the prince!
I assume you want the area of the region . . .
Calculate the area of the region determined by: .
We have: .
The graph is symmetric to the -axis, -axis and the origin
. . and has intercepts: .
The graph looks like a infinty-sign.Code:| * * | * * * * | * * * | * - * - - - - - - - * - - - - - - - * - * | * * * | * * * * | * * |
As skeeter pointed out, it is called a lemniscate.
The total area is: .