求证若p1 p2 p3三点的横坐标成等差数列,则对 - 知识问答

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.

1个回答

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

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