Question

已知圆C:(x-1)2+y2=9内有一点p(2,2)，过点p作直线l交圆C于A、B两点.当弦的长为四倍根号二

Answer 1

题不完全，假定为求直线的方程。设直线方程为ax + by + c = 0 (a, b不同时为0)
过P(2, 2): 2a + 2b + c = 0, c = -2(a + b)
ax + by - 2(a + b) = 0

圆C的圆心为C(1, 0)，半径r = 3

令AB的中点为M, CA² = CM² + AM²

3² = CM² + (4√2/2)²
CM² = 9 - 8 = 1
CM = 1
CM = |a - 2(a + b)|/√(a² + b²) = 1
|a + 2b| = √(a² + b²)
a² + 4ab + 4b² = a² + b²
4ab + 3b² = 0
b(4a + 3b) = 0
b = 0, 直线方程ax - 2a = 0, x = 2
b = -4a/3, 直线方程: ax -4ay/3 + 2/3 = 0, 3x - 4y + 2 = 0