实数xy满足x^2+(y+4)^2=4,则（x-1）^2+(y-1)^2的最大值是多少

Question

实数xy满足x^2+(y+4)^2=4,则（x-1）^2+(y-1)^2的最大值是多少

Answer 1

令y=-4+2sina
则x²+4sin²a=4
x²=4cos²a
x=2cosa
原式=(2cosa-1)²+(-5+2sina)²
=4cos²a+4sin²a-20sina-4cosa+26
=4-4(5sina-cosa)+26
=-4*√(5²+1²)sin(a-b)+30
=-4√26sin(a-b)+30
其中tanb=1/5
所以最大值=4√26+30