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2016年福建省高一数学竞赛15题是:如图1,圆O的圆心在坐标原点,过点P(0,1)的动直线l与圆O相交于A、B两点.当直线l平行于x轴时,直线l被圆O截得的线段长为■.(1)求圆O的方程;(2)在平面直角坐标系xOy内,是否存在与点P不同的定点Q,使得|QA|/|PA|=恒成|QB|/|PB|立?若存在,求出点Q的坐标;若不存在,请说明理由.本题(2)问是一道以圆为背景的定点问
As shown in Figure 1, the center of the circle O is at the origin of the coordinates, and the moving line l through point P (0,1) intersects the circle O at two points A and B. When the straight line l (1) Find the equation of the circle O; (2) In the plane Cartesian coordinate system xOy, there is a fixed point Q different from the point P, so that QA | / | PA | = constant | QB | / | PB | if present, find the coordinates of the point Q, if not, please explain the reasons. (2) Q is a round as the background of the fixed point ask