题目应改为
圆C经过点A(2,-1),和直线x+y-1=0相切,且圆心在直线y=-2x上,求圆C的方程.
设圆心C(a,-2a),依题意
|a-2a-1|/√2=√[(a-2)^2+(1-2a)^2],
平方,化简得a^2+2a+1=2(5a^2-8a+5),
整理得9a^2-42a+9=0,
3a^2-14a+3=0,
a=(7土2√10)/3,
半径r=(a+1)/√2=(5√2土2√5)/3,
∴圆C的方程是[x-(7+2√10)/3]^2+[y+2(7+2√10)/3]^2=[(5√2+2√5)/3]^2,
或[x-(7-2√10)/3]^2+[y+2(7-2√10)/3]^2=[(5√2-2√5)/3]^2.