求以点C(1,-1)为圆心且与直线x-y+6=0相切的圆的标准方程,求过程!!!

2025-03-10 01:46:55
推荐回答(1个)
回答1:

C(1,-1)为圆心
(x-1)^2 +(y+1)^2 =r^2 (1)
2x+2ydy/dx =0
dy/dx = -y/x = 1
=> x= -y (2)

x-y+6=0 (3)

sub (2) into (3)
2x+6=0
x=3

from (2)
y=-3

(3,-3) into (1)
(x-1)^2 +(y+1)^2 =r^2
r^2 = 4+4 =8

equation of circle
(x-1)^2 +(y+1)^2 =8