x^2/a^2+y^2/b^2=1
P到兩焦點(diǎn)的距離的和等于6,
所以2a=6
a=3
e=c/a=√6/3
c=√6
所以b^2=a^2-c^2=3
x^2/9+y^2/3=1
F1(-√6,0),F2(√6,0)
F1F2=2√6
P(m,n)
PF1垂直PF2
所以PF1^2+PF2^2=F1F2^2
(m+√6)^2+n^2+(m-√6)^2+n^2=24
2m^2+2n^2=12
m^2+n^2=6
P在橢圓上
所以m^2/9+n^2/3=1
m^2+3n^2=9
所以n^2=3/2,m^2=9/2
|n|=√6/2
所以面積等于|F1F2|*|n|/2=3
P有四解(3√2/2,√6/2)
(-3√2/2,√6/2)
(3√2/2,-√6/2)
(-3√2/2,-√6/2)