如图，点在抛物线上，过点作与轴平行的直线交抛物线于点，延长分别与抛物线相交于点...

如图，点在抛物线上，过点作与轴平行的直线交抛物线于点，延长分别与抛物线相交于点，连接，设点的横坐标为，且．

(1).当时，求点的坐标；

(2).当为何值时，四边形的两条对角线互相垂直；

(3).猜想线段与之间的数量关系，并证明你的结论．

【解析】（1）点在抛物线上，且，，······························ 1分点与点关于轴对称，．························································ 2分设直线的解析式为，．······················································································· 3分解方程组，得．································································· 4分（2）当四边形的两对角线互相垂直时，由对称性得直线与轴的夹角等于所以点的横、纵坐标相等， 5分这时，设，代入，得，．即当时，四边形的两条对角线互相垂直．········································· 6分（3）线段．········································································································ 7分点在抛物线，且，得直线的解析式为，解方程组，得点······················································· 8分由对称性得点，··················································· 9分，． 10分【解析】略

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