椭圆X2/a2十Y2/b2=1(a>b>0)的右焦点为F,右顶点、上顶点分别为A、B,且...椭圆X2/a2十Y2/b2=1(a>b>0)的右焦点为F,右顶点、上顶点分别为A、B,且丨AB丨=√5/2丨BF丨求离心率

Question

椭圆X2/a2十Y2/b2=1(a>b>0)的右焦点为F,右顶点、上顶点分别为A、B,且...
椭圆X2/a2十Y2/b2=1(a>b>0)的右焦点为F,右顶点、上顶点分别为A、B,且丨AB丨=√5/2丨BF丨 求离心率

Answer 1

c^2+b^2=a^2,BF=a-c,e=c/a,AB=√(b^2+a^2),√(b^2+a^2)=√5/2(a-c),b^2+a^2=5/4(a^2-2ac+c^2),
2a^2-c^2=5/4(a^2-2ac+c^2),3/4a^2-9/4c^2+5/2ac=0,3/4-9/4e^2+5/2e=0,e=5/9+2√13/9