x2+4y2=4x
x²-4x+4y²=0
(x-2)²+4y²=4
0≤x≤4
-1≤y≤1
x2+4y2=4x得y²=(4x-x²)/4
x²-y²
=x²-(4x-x²)/4
=5x²/4-x
=(5/4)(x²-4x/5)
=(5/4)(x-2/5)²-1/5
当x=2/5时,x²-y²有最小值为-1/5
当x=4时,x²-y²有最大值为16
因为平方值都是大于等于零(x-2)²+4y²=44y²≥0,所以(x-2)²≤4,可得0≤x≤4(x-2)²≥0,所以4y²≤4,可得-1≤y≤1