x^2+y^2=2x
（x-1)^2+y^2=1
令x=sina+1,y=cosa
xy=(sina+1)cosa=sinacosa+cosa
(xy)'=(cosa)^2-(sina)^2-sina
=-2(sina)^2-sina+1
=-(sina+1)(2sina-1)
令(xy)'=0
sina=-1或sina=1/2
-1≤sina≤1/2時,(xy)'≥0,函數(shù)單調(diào)遞增；
sina=-1時,有(xy)min=0sina=1/2時,有(xy)max=3√3/4
1/2≤sina≤1時,（xy)'≤0,函數(shù)單調(diào)遞減.
sina=1/2時,有(xy)max=3√3/4 sina=1時,有(xy)min=0
因此
0≤x^2y^2≤（3√3/4)^2
0≤x^2y^2≤27/16
x^2y^2的取值范圍為[0,27/16]