Question

已知P是以F1F2为焦点的椭圆x2/a2+y2/b2=1上的一点,若向量PF1乘以向量PF2=0,tan∠PF1F2=1

Answer 1

向量PF1乘以向量PF2=0

则：角F1PF2=90

所以tan∠PF1F2=PF2/PF1=1/2

PF1=2PF2

PF!+PF2=3PF2=2a

a=3PF2/2

F1F2=根号（PF1^2+PF2^2）=根号（PF2^2+4PF2^2)=PF2根号5=2c

c=PF2根号5/2

c/a=(根号5/2)/(3/2)=根号5/3