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