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文[1]介绍了椭圆x2a2+y2b2 =1焦点三角形的7个性质,笔者读后深受启发,经过研究,笔者也得到了椭圆焦点三角形的若干性质,作为对文[1] 的补充.图1设∠F1PF2 =θ,椭圆的离心率为 e.性质8 | PF1 |·| PF2 |=2b21+cosθ.证明 如图 1,由余弦定理,有| PF1 |2+| PF2 |2-2| PF1 |
In [1], we introduce seven properties of the focal triangle of x2a2 + y2b2 = 1, which are inspired by the author. After researching, the author also obtained some properties of the elliptical focal triangle, as a supplement to the paper [1]. 1 Suppose ∠F1PF2 = θ and the eccentricity of the ellipse is e. Properties 8 | PF1 | · | PF2 | = 2b21 + cosθ. Proof As shown in Figure 1, by the cosine theorem, | PF1 | 2+ | PF2 | 2-2 | PF1 |