2016年全国高中数学联赛解析几何试题为:如图1所示,在平面直角坐标系xOy中,F是x轴正半轴上的一个动点.以F为焦点、O为顶点作抛物线C.设P是第一象限内C上的一点,Q是x轴负半轴上一点,使得PQ为C的切线,且|PQ|=2.圆C_1、C_2均与直线OP相切于点P,且均与x轴相切.求点F的坐标,使圆C_1与C_2的面积之和取得最 In 2016, the National High School Maths League analytic geometry test questions as follows: As shown in Figure 1, F is a moving point on the positive x-axis of the x-axis in Cartesian coordinate system X. F is the focal point and O is the parabola C at the vertex. Let P be a point on C in the first quadrant, Q be a point on the negative half-axis of the x-axis such that PQ is a tangent to C and | PQ | = 2. Both circles C_1 and C_2 are tangent to line P at point P, And are tangent to the x-axis. Find the coordinates of point F such that the sum of the areas of circles C_1 and C_2 is the most