如图 1 ,设Ｆ1,Ｆ2 是双曲线ｘ2ａ2 -ｙ2ｂ2 =1 (ａ0 ,ｂ0 )的焦点 ,Ｐ是双曲线上的任意一点 (异于实轴端点 ) ,则称△Ｆ1ＰＦ2 为双曲线的焦点三角形 .图 1设∠Ｆ1ＰＦ2 =θ,∠ＰＦ1Ｆ2 =α,∠ＰＦ2 Ｆ1=β ,双曲线的离心率为ｅ,则△Ｆ1ＰＦ2 具有如下的性质 .定理 1｜ＰＦ1 As shown in Fig. 1, let F1, F2 be the focal point of the hyperbola x2a2 -y2b2 =1 (a0, b0) and P be any point on the hyperbola (different from the endpoint of the real axis), then we call △F1PF2 the hyperbolic focal triangle Fig. 1 Let ∠F1PF2 = θ, ∠PF1F2 = α, ∠ PF2 F1 = β, the eccentricity of the hyperbola is e, then △F1PF2 has the following properties. Theorem 1 | PF1