Question

已知圆C过两点A(-2,1),B(-1,0) 且圆心在直线3x-y-2=0上,过点D(-3,-6)

Answer 1

直线3x-y-2=0,y = 2 - 3x,C(c,2 -3c)

CA² = CB²

(c+2)² + (2-3c-1)² = (c+1)² + (2-3c-0)²

c = 3/2

C(3/2,-5/2)

半径r,r² = (3/2 +1)² + (-5/2-0)² = 25/2

r = 5/√2

设切线斜率为k,方程为y + 6 = k(x+3),kx -y + 3k -6 = 0

C与l的距离d等于半径

d = |3k/2 + 5/2 + 3k -6|/√(k² + 1) = 5/√2

31k² - 126k - 1 = 0

k = (63 ± 10√10)/31