题文
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. |
题型:解答题 难度:中档
答案
解:(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 |
据专家权威分析,试题“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..”主要考查你对 二次函数的定义,二次函数的图像,二次函数的最大值和最小值,求二次函数的解析式及二次函数的应用 等考点的理解。关于这些考点的“档案”如下:
二次函数的定义二次函数的图像二次函数的最大值和最小值求二次函数的解析式及二次函数的应用
考点名称:二次函数的定义 考点名称:二次函数的图像 考点名称:二次函数的最大值和最小值 考点名称:求二次函数的解析式及二次函数的应用
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