已知x^2+y^2-4x+y+4又4分之一=0求x^2+9y^2

题目

已知x^2+y^2-4x+y+4又4分之一=0求x^2+9y^2

答案

x²+y²-4x+y+4又1/4=0
(x²-4x+4)+(y²+y+1/4)=0
(x-2)²+(y+1/2)²=0
x-2=0 且 y+1/2=0
x=2 ,y=-1/2
x²+9y²=2²+9×(-1/2)²
=4+9×1/4
=4+9/4
=25/4