(1)|AF2|+|BF2|=2|AB|
两边同时加上|AF1|+|BF1|
|AF1|+|BF1|+|AF2|+|BF2|=2|AB|+|AF1|+|BF1|
4a=3|AB|,|AB|=4a/3
直线L:y=x+c,与椭圆方程联立得
(a^2+b^2)x^2+2a^2cx+a^2c^2-a^2b^2=0
|AB|=√(1+k^2)|x1-x2|
=√2*√[(x1+x2)^2-4x1x2] (带入两根之和,两根之积)
=4ab^2/(a^2+b^2)
4ab^2/(a^2+b^2)= 4a/3,
a^2=2b^2=b^2+c^2,b=c,a=√2c,e=√2/2
(2)取AB的中点M,M((x1+x2)/2,(y1+y2)/2)
(x1+x2)/2=-a^2c/(a^2+b^2)
(y1+y2)/2=(x1+c+x2+c)/2=(x1+x2)/2+c=b^2c/(a^2+b^2)
|PA|=|PB|,PM⊥AB,kPM=-1,
kPM=[ b^2c/(a^2+b^2)+1]/[ -a^2c/(a^2+b^2)]=-1
a^2c=a^2+b^2+b^2c (b=c,a=√2c)
2c^3=2c^2+c^2+c^3,c=3,a=3√2,b=3,
椭圆方程x^2/18+y^2/9=1