1一道试题及疑问如图1,已知A,B,C是长轴长为4的椭圆上的三点,点A是长轴的一个端点,BC过椭圆中心O,且AC·BC=0,|BC|=2|AC|,(1)建立适当的坐标系,求椭圆方程;(2)如果椭圆上有两点P,Q,使∠PCQ的平分线垂直于AO,证明:存在实数λ,使PQ=λAB.该题的解答如下:(1)以O为原点,OA为x轴建立 1 A test questions and questions As shown in Figure 1, known A, B, C is a long axis 4 oval on the three o’clock, A point is the long axis of the end, BC oval center O, and AC · BC = 0 , | BC | = 2 | AC |, (1) to establish an appropriate coordinate system, find the elliptic equation; (2) If there are two points on the ellipse P, Q, λ, so that PQ = λAB. The answer to the question is as follows: (1) O as the origin, OA for the x-axis