求证若p1 p2 p3三点的横坐标成等差数列,则对应的三点的半径也成等差数列.椭圆上任意一点与交点所在的线段叫做这点的交半径,设椭圆b^2x^2+a^2y^2=a^2b^2(a>b>0)上有三个点p1 p2 p3,F1 F2为左右交点.
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![求证若p1 p2 p3三点的横坐标成等差数列,则对应的三点的半径也成等差数列.椭圆上任意一点与交点所在的线段叫做这点的交半径,设椭圆b^2x^2+a^2y^2=a^2b^2(a>b>0)上有三个点p1 p2 p3,F1 F2为左右交点.](/uploads/image/z/11616745-49-5.jpg?t=%E6%B1%82%E8%AF%81%E8%8B%A5p1+p2+p3%E4%B8%89%E7%82%B9%E7%9A%84%E6%A8%AA%E5%9D%90%E6%A0%87%E6%88%90%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97%2C%E5%88%99%E5%AF%B9%E5%BA%94%E7%9A%84%E4%B8%89%E7%82%B9%E7%9A%84%E5%8D%8A%E5%BE%84%E4%B9%9F%E6%88%90%E7%AD%89%E5%B7%AE%E6%95%B0%E5%88%97.%E6%A4%AD%E5%9C%86%E4%B8%8A%E4%BB%BB%E6%84%8F%E4%B8%80%E7%82%B9%E4%B8%8E%E4%BA%A4%E7%82%B9%E6%89%80%E5%9C%A8%E7%9A%84%E7%BA%BF%E6%AE%B5%E5%8F%AB%E5%81%9A%E8%BF%99%E7%82%B9%E7%9A%84%E4%BA%A4%E5%8D%8A%E5%BE%84%2C%E8%AE%BE%E6%A4%AD%E5%9C%86b%5E2x%5E2%2Ba%5E2y%5E2%3Da%5E2b%5E2%28a%3Eb%3E0%29%E4%B8%8A%E6%9C%89%E4%B8%89%E4%B8%AA%E7%82%B9p1+p2+p3%2CF1+F2%E4%B8%BA%E5%B7%A6%E5%8F%B3%E4%BA%A4%E7%82%B9.)
求证若p1 p2 p3三点的横坐标成等差数列,则对应的三点的半径也成等差数列.椭圆上任意一点与交点所在的线段叫做这点的交半径,设椭圆b^2x^2+a^2y^2=a^2b^2(a>b>0)上有三个点p1 p2 p3,F1 F2为左右交点.
求证若p1 p2 p3三点的横坐标成等差数列,则对应的三点的半径也成等差数列.
椭圆上任意一点与交点所在的线段叫做这点的交半径,设椭圆b^2x^2+a^2y^2=a^2b^2(a>b>0)上有三个点p1 p2 p3,F1 F2为左右交点.求证若p1 p2 p3三点的横坐标成等差数列,则对应的三点的半径也成等差数列
求证若p1 p2 p3三点的横坐标成等差数列,则对应的三点的半径也成等差数列.椭圆上任意一点与交点所在的线段叫做这点的交半径,设椭圆b^2x^2+a^2y^2=a^2b^2(a>b>0)上有三个点p1 p2 p3,F1 F2为左右交点.
交半径
=√ (x-c)^2+y^2
=√ (x-c)^2+b^2-b^2x^2/a^2
=√(c^2*x^2/a^2 -2cx +a^2)
= a - (c/a)x
p1 p2 p3三点的横坐标成等差数列,2x2 = x1+x3
|P1F| + |P3F|
= a - (c/a)x1 +a - (c/a)x3
= 2a-(c/a)(x1+x3)
= 2a -2(c/a)x2
= 2|P2F|
三点的半径也成等差数列