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椭圆x^2/9+y^2/4=1
a=3,b=2,c=根号5
A坐标是(0,-2)
PF1,PA,PF2成等差数列,则有2PA=PF1+PF2=2a
即PA=a=3.
设P坐标是(m,n),则有PA^2=(m-0)^2+(n+2)^2=9
4m^2+9n^2=36
4m^2+4(n^2+4n+4)=36
9n^2=4n^2+16n+16
5n^2-16n-16=0
(5n+4)(n-4)=0
n=-4/5,n=4
n=-4/5时有m^2+36/25=9,m^2=189/25
m=(+/-)3/5根号21
n=4时有m^2=9-36
1年前
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