橢圓的焦距是長(zhǎng)軸長(zhǎng)與短軸長(zhǎng)的等比中項(xiàng)
設(shè)焦距|F1F2|=2c
長(zhǎng)軸長(zhǎng)=2a
短軸長(zhǎng)=2b
比例中項(xiàng)
(2c)^2=4a*b
c^2=a*b
e=a/c=√(a^2/c^2)=√ab/a^2=√b/a
b^2=a^2-c^2
a^2-ab-b^2=0
同除ab
a/b-b/a=1
令b/a=x
x^2+x=1
(x+1/2)=5/4
x=√(5-1)/2
e=√(b/a)=√x=√[(5-1)/2]