Question

圆心为(2,3)且与直线X+Y-1=0相切的圆的方程是

Answer 1

圆心到直线距离=半径
|2+3-1|/√(1²+1²)=4/√2
(4/√2)²=8
圆的方程为(x-2)²+(y-3)²=8

一楼的方法是正确的，不过距离公式错了，所以结果也就错了。

距离公式：
点(x，y)到直线ax+by+c=0的距离d=|ax+by+c|/√(a²+b²)

Answer 2

C= (2,3)
x+y-1 = 0 (1)
y = -x +1
slope = -1
r = distance between (2,3) and the line x+y-1=0
let M be a point on the line x+y-1=0 such that CM perpendicular to the line x+y-1=0
equation of CM
(y-3)/(x-2) = 1
x-y+1 =0 (2)
(1) +(2)
2x = 0
x=0
y =1
M(0,1)
r^2 = |CM|^2
= ((2-0)^2+(3-1))^2)
= 8

equation of circle:
(x-2)^2 +(y-3)^2 = 8

Answer 3

圆心(2,3)到直线x+y-1=0的距离=|2+3-1|/√13=4/√2=2√2。
圆方程为：(x-2)^2+(y-3)^2=8。