Question

点A,F分别是椭圆x2/a2+y2/b2=1(a>b>0)的上顶点和右焦点,直线AF与椭圆交于另一点B,

Answer 1

设c=1 ,那么AO² = b² = a² - 1

AO² = OF×OQ

OQ=a² - 1

过P做x轴的垂线交x轴于M,

PM/AO=PQ/AQ=5/13

PM=5√（a²-1） / 13

把点P带入椭圆算出P点横坐标=12a/13

MQ/OQ=PQ/AQ=5/13

(a²-1-12a/13)/(a²-1) = 5/13

2a² -3a -2 =0

a=2

椭圆的离心率=c/a=1/2