双曲线实轴为2a,F1F2为其焦点,弦AB过F1且|AF1|,|AB|,|BF2|成等差数列,求|AB|
问题描述:
双曲线实轴为2a,F1F2为其焦点,弦AB过F1且|AF1|,|AB|,|BF2|成等差数列,求|AB|
答
2|AB| = |BF2| + |AF1|
|AB| = |AF1| + |BF1|
|AB| + |AF1| + |BF1| = |BF2| + |AF1|
|AB| = |BF2| - |BF1| = 2a
最后一步是双曲线的定义