Question

过点A(4,1)的圆C与直线x-y-1=0相切于点B(2,1),求圆C方程

Answer 1

圆心C在直线x+y-3=0上
设C坐标（x0,3-x0)
r^2=BC^2=(x0-2)^2+(2-x0)^2=2(x0-2)^2=AC^2=(x0-4)^2+(2-x0)^2
(x0-2)^2=(x0-4)^2
x0=3
点C(3, 0)，半径r^2=2
圆C方程
(x-3)^2+y^2=2

Answer 2

设圆心O(a,b)
|OB|=r
O到直线x-y-1=0的距离=r
|a-b-1|/根2=r
(x-a)^2+(y-b)^2=r^2
圆过点A(4,1)点B(2,1)
(4-a)^2+(1-b)^2=r^2
(2-a)^2+(1-b)^2=r^2
(4-a)^2=(2-a)^2
a=3
|3-b-1|/根2=r
b=-2
r^2=8
(x-3)^2+(y+2)^2=8