What's the maximum and minimum of f(x,y)=xy with the constraint
$$\dfrac{(x-x_o)^2 }{A^2} + \dfrac{(y-y_o)^2 }{B^2} = 1$$
Using lagrangian multipliers is simple when the center of the ellipse is the origin, but when it's off-center I get complicated equations I can't solve. I also tried parametrizing it, but I didn't get anywhere. Does anyone have any ideas?