ρ=3/(4-2cosa)
√(x^2+y^2)=3/[4-x/√(x^2+y^2)]
4√(x^2+y^2)-x=3
4√(x^2+y^2)=x+3
两边平方
16x^2+16y^2=x^2+6x+9
15x^2-6x+16y^2=9
15(x-1/5)^2+16y^2=9-3/5=42/5
(x-1/5)^2/(14/25)+y^2/(21/40)=1
14/25>21/40
所以a^2=14/25,b^2=21/40
c^2=a^2-b^2=7/200
c=√14/20
所以焦距=2c=√14/10