椭圆x²/a²+y²/b²=1(a>b>0)的两焦点为F1,F2,椭圆上存在一点p,是PF1⊥PF2,
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![椭圆x²/a²+y²/b²=1(a>b>0)的两焦点为F1,F2,椭圆上存在一点p,是PF1⊥PF2,](/uploads/image/z/11466639-63-9.jpg?t=%E6%A4%AD%E5%9C%86x%26%23178%3B%2Fa%26%23178%3B%2By%26%23178%3B%2Fb%26%23178%3B%3D1%EF%BC%88a%EF%BC%9Eb%EF%BC%9E0%EF%BC%89%E7%9A%84%E4%B8%A4%E7%84%A6%E7%82%B9%E4%B8%BAF1%2CF2%2C%E6%A4%AD%E5%9C%86%E4%B8%8A%E5%AD%98%E5%9C%A8%E4%B8%80%E7%82%B9p%2C%E6%98%AFPF1%E2%8A%A5PF2%2C)
椭圆x²/a²+y²/b²=1(a>b>0)的两焦点为F1,F2,椭圆上存在一点p,是PF1⊥PF2,
椭圆x²/a²+y²/b²=1(a>b>0)的两焦点为F1,F2,椭圆上存在一点p,是PF1⊥PF2,
椭圆x²/a²+y²/b²=1(a>b>0)的两焦点为F1,F2,椭圆上存在一点p,是PF1⊥PF2,
椭圆定义
PF1+PF2=2a
(PF1+PF2)²=4a²
(PF1)²+2PF1*PF2+(PF2)²=4a²
又PF1垂直于PF2
即 (F1F2)²=(PF1)²+(PF2)²=4c²
2PF1*PF2≤(PF1)²+(PF2)²
即 4a²≤ 4c²+4c²
a²≤2c²
2e²≥1 e∈(0,1)
解得√2/2 ≤e<1