设F1和F2分别是椭圆x²/9+y²/4=1的左焦点又焦点,A是该椭圆与Y轴负半轴的交点,子啊椭圆上求点P使得丨PF1丨、丨PA丨丶丨PF2丨成等差数列PF1+PF2=6 A(0、-2) ,PA=3,x²+(y+2)²=9又x²/9+y
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![设F1和F2分别是椭圆x²/9+y²/4=1的左焦点又焦点,A是该椭圆与Y轴负半轴的交点,子啊椭圆上求点P使得丨PF1丨、丨PA丨丶丨PF2丨成等差数列PF1+PF2=6 A(0、-2) ,PA=3,x²+(y+2)²=9又x²/9+y](/uploads/image/z/13385323-19-3.jpg?t=%E8%AE%BEF1%E5%92%8CF2%E5%88%86%E5%88%AB%E6%98%AF%E6%A4%AD%E5%9C%86x%26%23178%3B%2F9%2By%26%23178%3B%2F4%3D1%E7%9A%84%E5%B7%A6%E7%84%A6%E7%82%B9%E5%8F%88%E7%84%A6%E7%82%B9%2CA%E6%98%AF%E8%AF%A5%E6%A4%AD%E5%9C%86%E4%B8%8EY%E8%BD%B4%E8%B4%9F%E5%8D%8A%E8%BD%B4%E7%9A%84%E4%BA%A4%E7%82%B9%2C%E5%AD%90%E5%95%8A%E6%A4%AD%E5%9C%86%E4%B8%8A%E6%B1%82%E7%82%B9P%E4%BD%BF%E5%BE%97%E4%B8%A8PF1%E4%B8%A8%E3%80%81%E4%B8%A8PA%E4%B8%A8%E4%B8%B6%E4%B8%A8PF2%E4%B8%A8%E6%88%90%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97PF1%2BPF2%3D6+A%280%E3%80%81-2%29+%2CPA%3D3%2Cx%26%23178%3B%2B%EF%BC%88y%2B2%EF%BC%89%26%23178%3B%3D9%E5%8F%88x%26%23178%3B%2F9%2By%26%231)
设F1和F2分别是椭圆x²/9+y²/4=1的左焦点又焦点,A是该椭圆与Y轴负半轴的交点,子啊椭圆上求点P使得丨PF1丨、丨PA丨丶丨PF2丨成等差数列PF1+PF2=6 A(0、-2) ,PA=3,x²+(y+2)²=9又x²/9+y
设F1和F2分别是椭圆x²/9+y²/4=1的左焦点又焦点,A是该椭圆与Y轴负半轴的交点,子啊椭圆上求点P
使得丨PF1丨、丨PA丨丶丨PF2丨成等差数列
PF1+PF2=6 A(0、-2) ,PA=3,
x²+(y+2)²=9又x²/9+y²/4=1,(y+2)²/9-y²/4=0x²+(y+2)²=9这步怎么来的
设F1和F2分别是椭圆x²/9+y²/4=1的左焦点又焦点,A是该椭圆与Y轴负半轴的交点,子啊椭圆上求点P使得丨PF1丨、丨PA丨丶丨PF2丨成等差数列PF1+PF2=6 A(0、-2) ,PA=3,x²+(y+2)²=9又x²/9+y
设椭圆上的点P(x,y),
∵|PF1|、|PA|、|PF2|成等差数列,
∴2|PA|=|PF1|+|PF2|=2a=6
∴|PA|=3,即|PA|²=9
∵A(0,-2),∴(x-0)²+(y+2)²=9,即x²+(y+2)²=9,
两边同除以9,得x²/9+(y+2)²/9=1①,
又∵x²/9+y²/4=1②,
∴②-①,得(y+2)²/9-y²/4=0,可求得y=4或y=-4/5,
又-2≤y≤2,∴y=4舍去,
当y=-4/5时,x=±3√21/5,
故P(3√21/5,-4/5)或P(-3√21/5,-4/5).