已知实数x,y满足关系：x^2+y^2-4x+6y=0

(x-2)²+(y+3)²=13
令x-2=√13cosx
x=√13cosa+2
则(y+3)²=13-13cos²a=13sin²a
y+3=√13sina
y=-3+√13sina
x²+y²
=13cos²a+4√13cosa+4+13sin²a-6√13sina+9
=-6√13sina+4√13cosa+26
=-26sin(a-b)+26
其中tanb=4√13/6√13=2/3
所以sin(a-b)=-1
x²+y²最大=26+26=52