F₁,F₂是双曲线x²/9-y²/16=1的两个焦点,P在双曲线上且满足PF₁的绝对值×PF₂的绝对值=32,则角F₂PF₂等于?
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![F₁,F₂是双曲线x²/9-y²/16=1的两个焦点,P在双曲线上且满足PF₁的绝对值×PF₂的绝对值=32,则角F₂PF₂等于?](/uploads/image/z/1776063-39-3.jpg?t=F%26%238321%3B%2CF%26%238322%3B%E6%98%AF%E5%8F%8C%E6%9B%B2%E7%BA%BFx%26sup2%3B%2F9%EF%BC%8Dy%26sup2%3B%2F16%3D1%E7%9A%84%E4%B8%A4%E4%B8%AA%E7%84%A6%E7%82%B9%2CP%E5%9C%A8%E5%8F%8C%E6%9B%B2%E7%BA%BF%E4%B8%8A%E4%B8%94%E6%BB%A1%E8%B6%B3PF%26%238321%3B%E7%9A%84%E7%BB%9D%E5%AF%B9%E5%80%BC%C3%97PF%26%238322%3B%E7%9A%84%E7%BB%9D%E5%AF%B9%E5%80%BC%3D32%2C%E5%88%99%E8%A7%92F%26%238322%3BPF%26%238322%3B%E7%AD%89%E4%BA%8E%3F)
F₁,F₂是双曲线x²/9-y²/16=1的两个焦点,P在双曲线上且满足PF₁的绝对值×PF₂的绝对值=32,则角F₂PF₂等于?
F₁,F₂是双曲线x²/9-y²/16=1的两个焦点,P在双曲线上且满足PF₁的绝对值×PF₂的绝对值=32,则角F₂PF₂等于?
F₁,F₂是双曲线x²/9-y²/16=1的两个焦点,P在双曲线上且满足PF₁的绝对值×PF₂的绝对值=32,则角F₂PF₂等于?
a²=9
a=3
设PF1=m,PF2=n
则|m-n|=2a=6
平方
m²+n²-2mn=36
mn=32
所以m²+n²=100
c²=9+16=25
c=5
F1F2=2c=10
则m²+n²=F1F2²
所以F1PF2=90度