如圖,點在拋物線上,過點作與軸平行的直線交拋物線于點,延長分別與拋物線相交于點,連接,設(shè)點的橫坐標為,且

 (1).當(dāng)時,求點的坐標;

 

 (2).當(dāng)為何值時,四邊形的兩條對角線互相垂直;

(3).猜想線段之間的數(shù)量關(guān)系,并證明你的結(jié)論.

 

解:(1)在拋物線上,且,,······························ 1分

   與點關(guān)于軸對稱,.························································ 2分

   設(shè)直線的解析式為

   .······················································································· 3分

   解方程組,得.································································· 4分

(2)當(dāng)四邊形的兩對角線互相垂直時,由對稱性得直線軸的夾角等于所以點的橫、縱坐標相等,      5分

   這時,設(shè),代入,得

   即當(dāng)時,四邊形的兩條對角線互相垂直.········································· 6分

(3)線段.········································································································ 7分

   在拋物線,且,

   得直線的解析式為

   解方程組,得點······················································· 8分

   由對稱性得點,··················································· 9分

   

   .                                                      10分

 

解析:略

 

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