X^2+4Y^2=4X Y^2=(4X-X^2)/4 X^2-Y^2=X^2-(4X-X^2)/4 =5X^2/4-X=5(X-2/5)^2/4-1/5 又X^2+4Y^2=4X 即(X-2)^2+4Y^2=4 所以0≤X≤4 所以X=4时X^2-Y^2取得最大值,为16
