Question

已知定点F（1,0)和直线l1 y=1,过定点F与直线L相切的动圆圆心为点C

Answer 1

设C(x,y)

|CF| = C和直线l1的距离d,二者平方分别为:

|CF|² = (y - 1)²

d² = (x - 1)² + (y - 0)²

C的轨迹:(x- 1)² = 1- 2y

y = -x²/2 + x

设A(a,-a²/2 + a),B(b,-b²/2 + b)

OA斜率m = -a/2 + 1

OB斜率n = -b/2 + 1

OA垂直OB:(1 - a/2)(1 - b/2) = -1

ab = 4(a + b -2) (1)

AB的方程:

(y - a + a²/2)/(-b²/2 + b - a + a²/2) = (x - a)/(b - a)

整理:2y = (2 - a - b)x + ab = (2 - a - b)x + 4(a + b -2)

= (2 - a - b)(x - 4)

过一个定点(4,0)