设F1,F2为椭圆4x^2+9y^2=36的左右焦点A为椭圆与y轴负半轴交点,P为椭圆上点,求点P使lPF1l,lPAl,lPF2_数学解答

设F1,F2为椭圆4x^2+9y^2=36的左右焦点A为椭圆与y轴负半轴交点,P为椭圆上点,求点P使
lPF1l,lPAl,lPF2l成等差数列
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人气：202 ℃　时间：2019-08-20 11:45:24

解答

椭圆x^2/9+y^2/4=1a=3,b=2,c=根号5A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=94m^2+9n^2=364m^2+4(n^2+4n+4)=369n^2=4n^2+16n+165n^2-16n-16=0(5n+...