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椭圆x2/a2+y2/b2=1(a>b>0)中除长轴两端点外的任一点P(x1,y1)与两焦点F1(-c,0)、F2(c,0)所组成的三角形PF1 F2叫做焦点三角形 .焦半径|PF1|=a+ex1,|PF2|=a-ex1.焦点三角形具有不少有益的结论,而对这些结论的证明亦颇有启迪性;并且这些结论在解题中也能起到不少帮助. 1.△PF1F2的周长为定值. 这个结论显而易见.由椭圆定义知|PF1|+|PF2|=2a,而|F1F2|=2c,因此这个定值为2a+2c.
Any point P(x1,y1) and two focal points F1(-c,0) and F2(c,0) except the two ends of the major axis in the ellipse x2/a2+y2/b2=1(a>b>0) The composed triangle PF1 F2 is called the focal triangle. The focal radius |PF1|=a+ex1,|PF2|=a-ex1. The focal triangle has many useful conclusions, and the proof of these conclusions is also inspiring; These conclusions can also help a lot in solving problems. 1. The perimeter of ΔPF1F2 is a fixed value. This conclusion is obvious. It is known by the ellipse that |PF1|+|PF2|=2a, and |F1F2|=2c, So this fixed value is 2a+2c.